Mathematical Structures: History of Commutative residuated lattice-ordered semigroups

[Home]History of Commutative residuated lattice-ordered semigroups

HomePage | RecentChanges | Login

Revision 2 . . July 26, 2004 3:11 pm by Jipsen
Revision 1 . . July 25, 2004 12:04 pm by Jipsen
  
Difference (from prior major revision) (no other diffs)

Changed: 28,29c28,29
\Large Name of class
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit}
\Large Commutative residuated lattice-ordered semigroups
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Commutative_residuated_lattice-ordered_semigroups}{edit}

Changed: 31c31
\abbreviation{Abbr}
\abbreviation{CRLSgrp}

Changed: 34,39c34
A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle
...\rangle$ such that

$\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class}

$op_1$ is (name of property): $axiom_1$
A commutative residuated lattice-ordered semigroup is a \href{Residuated_lattice-ordered_semigroups.pdf}{residuated lattice-ordered semigroup} $\mathbf{A}=\langle A, \vee, \wedge, \cdot, \to\rangle$ such that

Changed: 41c36
$op_2$ is ...: $...$
$\cdot$ is commutative: $xy=yx$

Changed: 50,51c45,49
Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x ... y)=h(x) ... h(y)$
Let $\mathbf{A}$ and $\mathbf{B}$ be commutative residuated lattice-ordered semigroups. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x \vee y)=h(x) \vee h(y)$,
$h(x \wedge y)=h(x) \wedge h(y)$,
$h(x \cdot y)=h(x) \cdot h(y)$, and
$h(x \to y)=h(x) \to h(y)$.

Changed: 77c75
Classtype & (value, see description) \cite{Ln19xx} \\\hline
Classtype & variety \\\hline

Changed: 83,84c81,82
Congruence distributive & \\\hline
Congruence modular & \\\hline
Congruence distributive & yes \\\hline
Congruence modular & yes \\\hline

Changed: 119c117
\href{....pdf}{...} subvariety
\href{Commutative_distributive_residuated_lattice-ordered_semigroups.pdf}{Commutative distributive residuated lattice-ordered semigroups} subvariety

Changed: 121c119
\href{....pdf}{...} expansion
\href{Commutative_residuated_lattices.pdf}{Commutative residuated lattices} expansion

Changed: 127c125
\href{....pdf}{...} supervariety
\href{Residuated_lattice-ordered_semigroups.pdf}{Residuated lattice-ordered semigroups} supervariety

Changed: 129c127
\href{....pdf}{...} subreduct
\href{Commutative_lattice-ordered_semigroups.pdf}{Commutative lattice-ordered semigroups} subreduct
HomePage | RecentChanges | Login
Search: