If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.
@article{bwmeta1.element.doi-10_2478_s11533-006-0036-3,
author = {Xia Zhang and Valdis Laan},
title = {On homological classification of pomonoids by regular weak injectivity properties of S-posets},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {181-200},
zbl = {1143.06007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0036-3}
}
Xia Zhang; Valdis Laan. On homological classification of pomonoids by regular weak injectivity properties of S-posets. Open Mathematics, Tome 5 (2007) pp. 181-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0036-3/
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