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index.html [2018/04/28 14:35]
jipsen
index.html [2019/12/10 17:29] (current)
pnotthesamejipsen
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what properties are known about these structures. what properties are known about these structures.
-These pages are currently still under construction. Knowledgeable readers are encouraged to add or correct information. +These pages 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.+/*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 Initially the main content concerns mostly first-order classes of relational
structures and, more particularly, equationally defined classes of algebraic structures. 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 free to add some relevant information and references by using the edit
link on the respective page. Pages are written in DokuWiki syntax, but mathematical notation is in standard LaTeX. link on the respective page. Pages are written in DokuWiki syntax, but mathematical notation is in standard LaTeX.
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versions of these pages are still available at http://math.chapman.edu/cgi-bin/structures.pl and http://math.chapman.edu/cgi-bin/structures . 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 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.*/
**New:** Boldface links below display lists of finite algebras in a particular class (calculated locally in the browser). **New:** Boldface links below display lists of finite algebras in a particular class (calculated locally in the browser).
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  -[[Bilattices]]   -[[Bilattices]]
  -[[Bilinear algebras]]   -[[Bilinear algebras]]
-  -[[Basic logic algebras|BL-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]]**,   -[[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]] nbsp [[wp>Boolean algebra (structure)]]   -[[Boolean algebras]] nbsp [[wp>Boolean algebra (structure)]]
  -[[Boolean algebras with operators]]   -[[Boolean algebras with operators]]
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  -[[Cancellative commutative semigroups]]   -[[Cancellative commutative semigroups]]
  -[[Cancellative monoids]]   -[[Cancellative monoids]]
 +  -[[Cancellative partial monoids]]
  -[[Cancellative semigroups]]   -[[Cancellative semigroups]]
  -[[Cancellative residuated lattices]]   -[[Cancellative residuated lattices]]
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  -[[Commutative BCK-algebras]]   -[[Commutative BCK-algebras]]
  -[[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 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 integral ordered monoids]], **[[Finite commutative integral ordered monoids]]**
  -[[Commutative inverse semigroups]]   -[[Commutative inverse semigroups]]
 +  -[[Commutative involutive FL-algebras]]
 +  -[[Commutative involutive residuated posets]]
  -[[Commutative lattice-ordered monoids]]   -[[Commutative lattice-ordered monoids]]
  -[[Commutative lattice-ordered rings]]   -[[Commutative lattice-ordered rings]]
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  -[[Completely regular Hausdorff spaces]]   -[[Completely regular Hausdorff spaces]]
  -[[wp>Completely regular semigroups]]   -[[wp>Completely regular semigroups]]
 +  -[[Conjugative binars]]
  -[[Continuous lattices]]   -[[Continuous lattices]]
  -[[Continuous posets]]   -[[Continuous posets]]
  -[[Cyclic involutive FL-algebras]]   -[[Cyclic involutive FL-algebras]]
 +  -[[Cyclic involutive residuated posets]]
  -[[Cylindric algebras]]   -[[Cylindric algebras]]
  -[[De Morgan algebras]]   -[[De Morgan algebras]]
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  -[[Distributive double p-algebras]]   -[[Distributive double p-algebras]]
  -[[Distributive dual p-algebras]]   -[[Distributive dual p-algebras]]
 +  -[[Distributive involutive residuated lattices]]
  -[[Distributive lattice expansions]]   -[[Distributive lattice expansions]]
  -[[Distributive lattices]]   -[[Distributive lattices]]
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  -[[Generalized orthoalgebras]]   -[[Generalized orthoalgebras]]
  -[[Generalized pseudo-effect algebras]]   -[[Generalized pseudo-effect algebras]]
 +  -[[Generalized separation algebras]]
  -[[Gödel algebras]]   -[[Gödel algebras]]
  -[[Graphs]]   -[[Graphs]]
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  -[[Hilbert spaces]]   -[[Hilbert spaces]]
  -[[Hoops]]   -[[Hoops]]
 +  -[[Idempotent residuated lattices]]
 +  -[[Idempotent involutive residuated lattices]]
  -[[Idempotent semirings]]   -[[Idempotent semirings]]
  -[[Idempotent semirings with identity]]   -[[Idempotent semirings with identity]]
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  -[[Involutive lattices]]   -[[Involutive lattices]]
  -[[Involutive FL-algebras|Involutive residuated lattices]]   -[[Involutive FL-algebras|Involutive residuated lattices]]
 +  -[[Involutive residuated posets]]
  -[[Join-semidistributive lattices]]   -[[Join-semidistributive lattices]]
  -[[Semilattices|Join-semilattices]]   -[[Semilattices|Join-semilattices]]
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  -[[Lattices]]   -[[Lattices]]
  -[[Left cancellative semigroups]]   -[[Left cancellative semigroups]]
 +  -[[Left neofield]]
  -[[Lie algebras]]   -[[Lie algebras]]
 +  -[[Commutative residuated partially ordered monoids|Lineales]]
  -[[Goedel algebras|Linear Heyting algebras]]   -[[Goedel algebras|Linear Heyting algebras]]
  -[[Linear logic algebras]]   -[[Linear logic algebras]]
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  -[[Lukasiewicz algebras of order n]]   -[[Lukasiewicz algebras of order n]]
  -[[M-sets]]   -[[M-sets]]
 +  -[[Binars|Magmas]]
  -[[Medial groupoids]]   -[[Medial groupoids]]
  -[[Medial quasigroups]]   -[[Medial quasigroups]]
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  -[[Near-rings with identity]]   -[[Near-rings with identity]]
  -[[Near-fields]]   -[[Near-fields]]
 +  -[[Neofields]]
  -[[Nilpotent groups]]   -[[Nilpotent groups]]
  -[[Nonassociative relation algebras]]   -[[Nonassociative relation algebras]]
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  -[[p-groups]]   -[[p-groups]]
  -[[Partial groupoids]]   -[[Partial groupoids]]
 +  -[[Partial monoid]]
  -[[Partial semigroups]]   -[[Partial semigroups]]
  -[[Partially ordered groups]]   -[[Partially ordered groups]]
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  -[[Residuated partially ordered monoids]]   -[[Residuated partially ordered monoids]]
  -[[Residuated partially ordered semigroups]]   -[[Residuated partially ordered semigroups]]
 +  -[[Residuated partially ordered monoids|Residuated posets]]
 +  -[[Right residuated binars]]
 +  -[[Right hoops]]
 +  -[[Right quasigroups]]
  -[[Rings]]   -[[Rings]]
  -[[Rings with identity]]   -[[Rings with identity]]
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  -[[Semiassociative relation algebras]]   -[[Semiassociative relation algebras]]
  -[[Semidistributive lattices]]   -[[Semidistributive lattices]]
 +  -[[Semifields]]
  -[[Semigroups]], **[[Finite semigroups]]**   -[[Semigroups]], **[[Finite semigroups]]**
  -[[Monoids|Semigroups with identity]]   -[[Monoids|Semigroups with identity]]
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  -[[Semirings with identity and zero]]   -[[Semirings with identity and zero]]
  -[[Semirings with zero]]   -[[Semirings with zero]]
 +  -[[Separation algebras]]
  -[[Sequential algebras]]   -[[Sequential algebras]]
  -[[Sets]]   -[[Sets]]
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  -[[Steiner quasigroups]]   -[[Steiner quasigroups]]
  -[[Stone algebras]]   -[[Stone algebras]]
 +  -[[Sugihara algebras]]
 +  -[[Sugihara monoids]]
  -[[Symmetric relations]]   -[[Symmetric relations]]
  -[[T0-spaces]]   -[[T0-spaces]]