MathStructures
http://math.chapman.edu/~jipsen/structures/
2018-06-21T20:49:37-07:00MathStructures
http://math.chapman.edu/~jipsen/structures/
http://math.chapman.edu/~jipsen/structures/lib/images/favicon.icotext/html2018-05-06T07:33:44-07:00Peter Jipsenpartially_ordered_semigroups
http://math.chapman.edu/~jipsen/structures/doku.php/partially_ordered_semigroups?rev=1525617224&do=diff
Partially ordered semigroups
Abbreviation: PoSgrp
Definition
A <b><i>partially ordered semigroup</i></b> is a structure such that
is a semigroup
is a partially ordered set
is <b><i>orderpreserving</i></b>:
Morphisms
Let and be partially ordered monoids. A morphism from to is a function that is an orderpreserving homomorphism:
,
<b><i>Title</i></b><b>1</i></b>text/html2018-05-06T00:54:38-07:00Peter Jipsensemigroups
http://math.chapman.edu/~jipsen/structures/doku.php/semigroups?rev=1525593278&do=diff
Semigroups
Abbreviation: Sgrp
Definition
A <b><i>semigroup</i></b> is a structure , where is an infix binary operation, called the
<b><i>semigroup product</i></b>, such that
is associative: .
Morphisms
Let and be semigroups. A morphism from
to is a function that is a homomorphism:text/html2018-04-28T15:00:08-07:00Peter Jipsenflc-algebras
http://math.chapman.edu/~jipsen/structures/doku.php/flc-algebras?rev=1524952808&do=diff
FL$_c$-algebras
Abbreviation: FL$_c$
Definition
A <b><i>FL-algebra</i></b> is an FL-algebra such that
is <b><i>contractive</i></b>:
Remark: This is a template.
If you know something about this class, click on the 'Edit text of this page' link at the bottom and fill out this page.<b><i></i></b><b><i>Full Lambek calculus with contraction is undecidable</i></b><b>81</i></b>text/html2018-04-28T14:51:48-07:00Peter Jipsenflec-algebras
http://math.chapman.edu/~jipsen/structures/doku.php/flec-algebras?rev=1524952308&do=diff
FLe-algebras
Abbreviation: FL$_{ec}$
Definition
A <b><i>full Lambek algebra with exchange and contraction</i></b>, or <b><i>FLec-algebra</i></b>, is a FLe-algebras
such that
is contractive or square-increasing:
Remark:
Morphisms
Let and be FLec-algebras. A morphism from to is a function that is a homomorphism:text/html2018-04-28T14:35:39-07:00Peter Jipsenindex.html
http://math.chapman.edu/~jipsen/structures/doku.php/index.html?rev=1524951339&do=diff
Mathematical Structures
The webpages 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.text/html2017-10-02T10:57:02-07:00Peter Jipsenequations
http://math.chapman.edu/~jipsen/structures/doku.php/equations?rev=1506967022&do=diff
Syntax | Terms | Equations | Horn formulas | Universal formulas | First-order formulas | Theories
Here we list equations, with the shorter term on the right (if possible).
1 trivial equations: one-element algebras 2 identity operation: 3 involutive operation: 4 inverse operations: 5 inside absorption: 6 outside absorption: 7 order- operation: 8 -idempotent 9 constant operations: 10 left projection: right projection: 11 idempo…text/html2017-10-01T20:07:06-07:00Peter Jipsenhorn_formulas
http://math.chapman.edu/~jipsen/structures/doku.php/horn_formulas?rev=1506913626&do=diff
Syntax | Terms | Equations | Horn formulas | Universal formulas | First-order formulas | Theories
A list of atomic formulas, quasiequations and universal Horn formulas.
reflexive: transitive: antisymmetric: left cancellation: right cancellation: left R-preserving: right R-preserving: