Mathematical Structures: History of Commutative ordered semigroups

# History of Commutative ordered semigroups

 Revision 2 . . July 26, 2004 2:28 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

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

Changed: 34,37c34
 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}
 A commutative ordered semigroups is an \href{Ordered_semigroups.pdf}{ordered semigroup} $\mathbf{A}=\langle A,\cdot,\le\rangle$ such that

Changed: 39,41c36
 $op_1$ is (name of property): $axiom_1$ $op_2$ is ...: $...$
 $\cdot$ is commutative: $xy=yx$

Changed: 50,51c45,46
 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 ordered semigroups. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a orderpreserving homomorphism: $h(x \cdot y)=h(x) \cdot h(y)$ and $x\le y\implies h(x)\le h(y)$

Changed: 119,121c114
 \href{....pdf}{...} subvariety \href{....pdf}{...} expansion
 \href{Commutative_ordered_monoids.pdf}{Commutative ordered monoids} expansion

Changed: 127c120
 \href{....pdf}{...} supervariety
 \href{Ordered_semigroups.pdf}{Ordered semigroups} supervariety

Changed: 129c122
 \href{....pdf}{...} subreduct
 \href{Commutative_semigroups.pdf}{Commutative semigroups} subreduct