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--- start [2021/02/22 21:11]
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+++ start [2024/10/13 06:35] (current)
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@@ Line 1: / Line 1: @@
 ===== Mathematical Structures =====
-The webpages collected here list information about classes of
+====These pages have moved to GitHub====
+https://github.com/jipsen/AlgebraicCategories/blob/main/files/index.html.md
+The pages collected here list information about classes of
 mathematical structures. The aim is to have a central place to check
 what properties are known about these structures.
-//These pages are currently still under construction. Knowledgeable readers are encouraged to add or correct information.// To enable the edit button on each page, use the Login link (above) to log in or create an account.
+These pages have moved. Click the link above for the latest version. /*are currently still under construction. Knowledgeable readers are encouraged to email additions or corrections to Peter Jipsen add or correct information.*/
+/*To enable the edit button on each page, use the Login link (above) to log in or create an account.*/
 Initially the main content concerns mostly first-order classes of relational
 structures and, more particularly, equationally defined classes of algebraic structures.
-If you are familiar with some of these classes of structures, feel
+If you are familiar with some of these classes of structures and would like some information added, please email Peter Jipsen (jipsen@chapman.edu). [Account creation unfortunately had to be disabled.] /*feel
 free to add some relevant information and references by using the edit
-link on the respective page. Most pages are written in standard LaTeX (if
+link on the respective page. Pages are written in DokuWiki syntax, but mathematical notation is in standard LaTeX.
-you don't know LaTeX you should probably not edit these pages -- the previous non-LaTeX
+The previous
-version of these pages is still available at http://math.chapman.edu/cgi-bin/structures.pl ).
+versions of these pages are still available at http://math.chapman.edu/cgi-bin/structures.pl and http://math.chapman.edu/cgi-bin/structures .
 You can use this [[Sandbox]] page to try out editing (without worrying about deleting
-useful information).
+useful information).*/
-[[Suggestions or comments]]? Just follow the link and edit the page.
+/*[[Suggestions or comments]]? Just follow the link and edit the page.*/
-This front page can also be edited to add further classes of structures. A criterion
+**New:** Boldface links below display lists of finite algebras in a particular class (calculated locally in the browser).
+/*This front page can also be edited to add further classes of structures. A criterion
 for inclusion in this list is that there should be some journal publication or book
-where the class has been named and defined.
+where the class has been named and defined.*/
+[[Acknowledgements]] | [[Notation and terminology]] | [[Properties]] | [[Tools]] | [[Online books and lecture notes]]
-[[Acknowledgements]] | [[Notation and terminology]] | [[Properties]] |
+[[Varieties]] | [[Quasivarieties]] | [[Universal classes]] | [[First-order classes]] | [[Second-order classes]]
-[[Tools]] | [[Online books and lecture notes]]
-[[Varieties]] | [[Quasivarieties]] | [[Universal classes]] | [[First-order classes]] |
+[[Algebras]] | [[Logics]] | [[Syntax]] | [[Terms]] | [[Equations]] | [[Horn formulas]] | [[Universal formulas]] | [[First-order formulas]] /*| [[Theories]]*/
-[[Second-order classes]] | [[Logics]]
 === Alphabetical list of all classes ===
-  -[[Abelian groups]]
+  -[[Abelian groups]] nbsp [[wp>Abelian group]]
   -[[Abelian lattice-ordered groups]]
   -[[Abelian ordered groups]]
   -[[Abelian p-groups]]
   -[[Abelian partially ordered groups]]
-  -[[Action algebras]]
+  -[[Action algebras]] nbsp [[wp>Action algebra]]
   -[[Action lattices]]
   -[[Algebraic lattices]]
-  -[[Algebraic posets]]
+  -[[Algebraic posets]] nbsp [[wp>Algebraic poset]]
   -[[Algebraic semilattices]]
-  -[[Allegories]]
+  -[[Allegories]] nbsp [[wp>Allegory (category theory)]]
   -[[Almost distributive lattices]]
-  -[[Associative algebras]]
+  -[[Associative algebras]] nbsp [[wp>Associative algebra]]
-  -[[Banach spaces]]
+  -[[Banach spaces]] nbsp [[wp>Banach space]]
-  -[[Bands]]
+  -[[Bands]] nbsp [[wp>Band (mathematics)]], **[[Finite bands]]**
   -[[Basic logic algebras]]
-  -[[BCI-algebras]]
+  -[[BCI-algebras]] nbsp [[wp>BCI algebra]]
-  -[[BCK-algebras]]
+  -[[BCK-algebras]] nbsp [[wp>BCK algebra]]
   -[[BCK-join-semilattices]]
   -[[BCK-lattices]]
   -[[BCK-meet-semilattices]]
+  -[[Bilattices]]
   -[[Bilinear algebras]]
+  -[[Binars]], **[[Finite binars]], [[Finite binars with identity|with identity]], [[Finite binars with zero|with zero]], [[Finite binars with identity and zero|with identity and zero]]**,
   -[[Basic logic algebras|BL-algebras]]
-  -[[Boolean algebras]]
+  -[[Boolean algebras]] nbsp [[wp>Boolean algebra (structure)]]
   -[[Boolean algebras with operators]]
   -[[Boolean groups]]
@@ Line 68: / Line 77: @@
   -[[Brouwerian algebras]]
   -[[Brouwerian semilattices]]
-  -[[wp>C-star-algebras]]
+  -[[wp>C*-algebras]]
   -[[Cancellative commutative monoids]]
   -[[Cancellative commutative semigroups]]
   -[[Cancellative monoids]]
+  -[[Cancellative partial monoids]]
   -[[Cancellative semigroups]]
   -[[Cancellative residuated lattices]]
@@ Line 80: / Line 90: @@
   -[[Closure algebras]]
   -[[Commutative BCK-algebras]]
-  -[[Commutative groupoids]]
+  -[[Commutative binars]], **[[Finite commutative binars]], [[Finite commutative binars with identity|with identity]], [[Finite commutative binars with zero|with zero]], [[Finite commutative binars with identity and zero|with identity and zero]]**
+  -[[Commutative idempotent involutive residuated lattices]]
+  -[[Commutative integral ordered monoids]], **[[Finite commutative integral ordered monoids]]**
   -[[Commutative inverse semigroups]]
+  -[[Commutative involutive FL-algebras]]
+  -[[Commutative involutive residuated posets]]
   -[[Commutative lattice-ordered monoids]]
   -[[Commutative lattice-ordered rings]]
   -[[Commutative lattice-ordered semigroups]]
-  -[[Commutative monoids]]
+  -[[Commutative monoids]], **[[Finite commutative monoids]], [[Finite commutative monoids with zero]]**
   -[[Commutative ordered monoids]]
   -[[Commutative ordered rings]]
-  -[[Commutative ordered semigroups]]
+  -[[Commutative ordered semigroups]], **[[Finite commutative ordered semigroups]]**
   -[[Commutative partially ordered monoids]]
   -[[Commutative partially ordered semigroups]]
@@ Line 98: / Line 112: @@
   -[[Commutative rings]]
   -[[Commutative rings with identity]]
-  -[[Commutative semigroups]]
+  -[[Commutative semigroups]], **[[Finite commutative semigroups]], [[Finite commutative semigroups with zero|with zero]]**
   -[[Compact topological spaces]]
   -[[Boolean spaces|Compact zero-dimensional Hausdorff spaces]]
@@ Line 109: / Line 123: @@
   -[[Directed complete partial orders|Complete partial orders]]
   -[[Completely regular Hausdorff spaces]]
-  -[[Completely regular semigroups]]
+  -[[wp>Completely regular semigroups]]
+  -[[Conjugative binars]]
   -[[Continuous lattices]]
   -[[Continuous posets]]
+  -[[Cyclic involutive FL-algebras]]
+  -[[Cyclic involutive residuated posets]]
   -[[Cylindric algebras]]
   -[[De Morgan algebras]]
@@ Line 126: / Line 143: @@
   -[[Distributive double p-algebras]]
   -[[Distributive dual p-algebras]]
+  -[[Distributive involutive residuated lattices]]
   -[[Distributive lattice expansions]]
   -[[Distributive lattices]]
@@ Line 137: / Line 155: @@
   -[[Dunn monoids]]
   -[[Dynamic algebras]]
+  -[[Effect algebras]]
   -[[Medial groupoids|Entropic groupoids]]
   -[[Equivalence algebras]]
@@ Line 145: / Line 164: @@
   -[[FL-algebras]]
   -[[FLc-algebras]]
+  -[[Heyting algebras|FLcw-algebras]]
   -[[FLe-algebras]]
+  -[[FLec-algebras]]
+  -[[Heyting Algebras|FLecw-algebras]]
   -[[FLew-algebras]]
+  -[[FLi-algebras]]
+  -[[FLo-algebras]]
   -[[FLw-algebras]]
   -[[Frames]]
@@ Line 153: / Line 177: @@
   -[[Generalized BL-algebras]]
   -[[Generalized Boolean algebras]]
+  -[[Generalized effect algebras]]
   -[[Generalized MV-algebras]]
-  -[[Goedel algebras]]
+  -[[Generalized orthoalgebras]]
+  -[[Generalized pseudo-effect algebras]]
+  -[[Generalized separation algebras]]
+  -[[Gödel algebras]]
   -[[Graphs]]
   -[[Groupoids]]
@@ Line 163: / Line 191: @@
   -[[Hilbert spaces]]
   -[[Hoops]]
+  -[[Idempotent residuated lattices]]
+  -[[Idempotent involutive residuated lattices]]
   -[[Idempotent semirings]]
   -[[Idempotent semirings with identity]]
   -[[Idempotent semirings with identity and zero]]
   -[[Idempotent semirings with zero]]
-  -[[Implication algebras]]
+  -[[Tarski algebras|Implication algebras]]
   -[[Implicative lattices]]
   -[[Integral domains]]
-  -[[Integral ordered monoids]]
+  -[[Integral involutive FL-algebras]]
+  -[[Integral ordered monoids]], **[[finite integral ordered monoids]]**
   -[[Integral relation algebras]]
   -[[Integral residuated lattices]]
   -[[Intuitionistic linear logic algebras]]
   -[[Inverse semigroups]]
+  -[[Involutive FL-algebras]]
   -[[Involutive lattices]]
-  -[[Involutive residuated lattices]]
+  -[[Involutive FL-algebras|Involutive residuated lattices]]
+  -[[Involutive residuated posets]]
   -[[Join-semidistributive lattices]]
   -[[Semilattices|Join-semilattices]]
@@ Line 182: / Line 215: @@
   -[[Kleene algebras]]
   -[[Kleene lattices]]
+  -[[Kleene logic algebras]]
   -[[Residuated partially ordered semigroups|Lambek algebras]]
+  -[[Lattice effect algebras]]
+  -[[Lattice implication algebras]]
   -[[Lattice-ordered groups]]
   -[[Lattice-ordered monoids]]
@@ Line 189: / Line 225: @@
   -[[Lattices]]
   -[[Left cancellative semigroups]]
+  -[[Left neofield]]
   -[[Lie algebras]]
+  -[[Commutative residuated partially ordered monoids|Lineales]]
   -[[Goedel algebras|Linear Heyting algebras]]
   -[[Linear logic algebras]]
@@ Line 198: / Line 236: @@
   -[[Lukasiewicz algebras of order n]]
   -[[M-sets]]
+  -[[Binars|Magmas]]
   -[[Medial groupoids]]
   -[[Medial quasigroups]]
@@ Line 209: / Line 248: @@
   -[[Monadic algebras]]
   -[[Monoidal t-norm logic algebras]]
-  -[[Monoids]]
+  -[[Monoids]], **[[Finite monoids]], [[Finite monoids with zero|with zero]]**
+  -[[Monounary algebras]]
   -[[Moufang loops]]
   -[[Moufang quasigroups]]
@@ Line 217: / Line 257: @@
   -[[Multisets]]
   -[[MV-algebras]]
+  -[[MV-effect algebras]]
+  -[[m-zeroids]]
   -[[Neardistributive lattices]]
   -[[Near-rings]]
   -[[Near-rings with identity]]
   -[[Near-fields]]
+  -[[Neofields]]
   -[[Nilpotent groups]]
   -[[Nonassociative relation algebras]]
   -[[Bilinear algebras|Nonassociative algebras]]
   -[[Normal bands]]
+  -[[Normal valued lattice-ordered groups]]
   -[[Normed vector spaces]]
   -[[Ockham algebras]]
   -[[Order algebras]]
+  -[[Ordered abelian groups]]
   -[[Ordered fields]]
   -[[Ordered groups]]
@@ Line 233: / Line 278: @@
   -[[Ordered monoids with zero]]
   -[[Ordered rings]]
-  -[[Ordered semigroups]]
+  -[[Ordered semigroups]], **[[Finite ordered semigroups]], [[Finite ordered semigroups with zero]]**
+  -[[Ordered semilattices]], **[[Finite ordered semilattices]]**
   -[[Partially ordered sets|Ordered sets]]
   -[[Ore domains]]
+  -[[Orthoalgebras]]
   -[[Ortholattices]]
   -[[Orthomodular lattices]]
   -[[p-groups]]
   -[[Partial groupoids]]
+  -[[Partial monoid]]
   -[[Partial semigroups]]
   -[[Partially ordered groups]]
@@ Line 249: / Line 297: @@
   -[[FL-algebras|Pointed residuated lattices]]
   -[[Polrims]]
-  -[[Polyadic algebras]]
+  -[[wp>Polyadic algebras]]
   -[[Partially ordered sets|Posets]]
   -[[Post algebras]]
@@ Line 257: / Line 305: @@
   -[[Process algebras]]
   -[[Pseudo basic logic algebras]]
+  -[[Pseudo-effect algebras]]
   -[[Pseudo MTL-algebras]]
   -[[Pseudo MV-algebras]]
   -[[Pseudocomplemented distributive lattices]]
   -[[Pure discriminator algebras]]
+  -[[Quandles]]
   -[[Quantales]]
   -[[Quasigroups]]
   -[[Quasi-implication algebras]]
+  -[[Quasi-MV-algebra]]
   -[[Preordered sets|Quasi-ordered sets]]
   -[[Quasitrivial groupoids]]
@@ Line 282: / Line 333: @@
   -[[Residuated partially ordered monoids]]
   -[[Residuated partially ordered semigroups]]
+  -[[Residuated partially ordered monoids|Residuated posets]]
+  -[[Right residuated binars]]
+  -[[Right hoops]]
+  -[[Right quasigroups]]
   -[[Rings]]
   -[[Rings with identity]]
@@ Line 287: / Line 342: @@
   -[[Semiassociative relation algebras]]
   -[[Semidistributive lattices]]
-  -[[Semigroups]]
+  -[[Semifields]]
+  -[[Semigroups]], **[[Finite semigroups]]**
   -[[Monoids|Semigroups with identity]]
-  -[[Semigroups with zero]]
+  -[[Semigroups with zero]], **[[Finite semigroups with zero]]**
-  -[[Semilattices]]
+  -[[Semilattices]], **[[Finite semilattices]]**
-  -[[Semilattices with identity]]
+  -[[Semilattices with identity]], **[[Finite semilattices with identity]]**
   -[[Semilattices with zero]]
   -[[Semirings]]
@@ Line 297: / Line 353: @@
   -[[Semirings with identity and zero]]
   -[[Semirings with zero]]
+  -[[Separation algebras]]
   -[[Sequential algebras]]
   -[[Sets]]
   -[[Shells]]
   -[[Division rings|Skew-fields]]
-  -[[Skew_lattices]]
+  -[[Skew lattices]]
   -[[Small categories]]
   -[[Sober T0-spaces]]
   -[[Solvable groups]]
+  -[[Sqrt-quasi-MV-algebras]]
   -[[Stably compact spaces]]
   -[[Steiner quasigroups]]
   -[[Stone algebras]]
+  -[[Sugihara algebras]]
+  -[[Sugihara monoids]]
   -[[Symmetric relations]]
   -[[T0-spaces]]
@@ Line 319: / Line 379: @@
   -[[wp>Topological vector spaces]]
   -[[Torsion groups]]
+  -[[Abelian ordered groups|Totally ordered abelian groups]]
+  -[[Ordered groups|Totally ordered groups]]
   -[[Ordered monoids|Totally ordered monoids]]
   -[[Transitive relations]]

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