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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.
2
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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
|
tom 5
|
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.
3
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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
|
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.
4
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An investigation on hyperS-posets over ordered semihypergroups

76%
Tang J., Davvaz B., Xie X.-Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
37-56
EN
In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S-poset A, and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize the (strong) order-congruences by the ρ-chains, where ρ is a (strong) congruence on A. Moreover, we give a method of constructing order-congruences, and prove that every hyper S-subposet B of a hyper S-poset A is a congruence class of one order-congruence on A if and only if B is convex. In the sequel, we give some homomorphism theorems of hyper S-posets, which are generalizations of similar results in S-posets and ordered semigroups.
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