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1
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On homological classification of pomonoids by GP-po-flatness ofS-posets

100%
Liang X., Feng X., Luo Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
767-782
EN
In this paper, we introduce GP-po-flatness property of S-posets over a pomonoid S, which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.
2
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Generators in the category of S-posets

100%
Laan V.
Open Mathematics
|
2008
|
tom 6
|
nr 3
357-363
EN
The paper contains characterizations of generators and cyclic projective generators in the category of ordered right acts over an ordered monoid.
3
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On homological classification of pomonoids by regular weak injectivity properties of S-posets

100%
Zhang X., Laan V.
Open Mathematics
|
2007
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tom 5
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nr 1
181-200
EN
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.
4
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Erratum to “On homological classification of pomonoids by regular weak injectivity properties of S-posets”

100%
Zhang X., Laan V.
Open Mathematics
|
2009
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tom 7
|
nr 1
163-164
EN
The original version of the article was published in Central European Journal of Mathematics, 2007, 5(1), 181–200, DOI: 10.2478/s11533-006-0036-3. Unfortunately, the original version of this article contains a mistake: in Theorem 5.2 only conditions (i) and (ii) (and not (iii)) are equivalent. We correct the theorem and its proof.
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