On strongly flat and condition (P) S-posets

In this paper, we first present some homological classifications of pomonoids by using condition (P) and strongly flat properties. Unlike the case for acts, condition (P) and strongly flat coincide for cyclic right S -posets when all weakly right reversible convex subpomonoids of a pomonoid S are le...

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Bibliographic Details
Published in:Semigroup forum 2011-06, Vol.82 (3), p.530-541
Main Authors: Ershad, M., Khosravi, R.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Research Article
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Summary:In this paper, we first present some homological classifications of pomonoids by using condition (P) and strongly flat properties. Unlike the case for acts, condition (P) and strongly flat coincide for cyclic right S -posets when all weakly right reversible convex subpomonoids of a pomonoid S are left collapsible. Thereby we characterize pomonoids over which strong flatness and condition (P) imply some other flatness properties. Furthermore, we characterize a pomonoid over which every right S -poset has a strongly flat (condition (P)) cover.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-010-9283-5