Structures characterizing partially ordered sets, and their automorphism groups

✍ Scribed by Russell Belding

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 955 KB
• Volume: 27
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(79)90104-3

✦ Synopsis

Hy finding invariant embeddings of a partially ordered set X into the semigroups it is shown that the semigroup of order ideals of X. where the semigroup operation is set union, and the semigroup and semiring of order preserving maps from X into the positive cone D' of a partially tirdered integral domain D. all characterize X to within poset isomorphism. The automorphism grouts of the e~migroup of or&r ideals is isomorphic to the automorphism group of X. The same t,olds for the xmtring of order preserving maps from X into the non-negative integers. and this semiring is the closed linear span of its idempotents.