Mathematical Structures: History of Commutative residuated lattice-ordered semigroups

# History of Commutative residuated lattice-ordered semigroups

 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 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