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1
Content available remote

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
Content available remote

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
|
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.
4
Content available remote

On Multiset Ordering

100%
Bancerek G.
Formalized Mathematics
|
2016
|
tom 24
|
nr 2
95-106
EN
Formalization of a part of [11]. Unfortunately, not all is possible to be formalized. Namely, in the paper there is a mistake in the proof of Lemma 3. It states that there exists x ∈ M1 such that M1(x) > N1(x) and (∀y ∈ N1)x ⊀ y. It should be M1(x) ⩾ N1(x). Nevertheless we do not know whether x ∈ N1 or not and cannot prove the contradiction. In the article we referred to [8], [9] and [10].
5
Content available remote

Conditions for strong Morita equivalence of partially ordered semigroups

100%
Tart L.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1100-1113
EN
We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.
6
Content available remote

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.
7
Content available remote

Fuzzy ideals of ordered semigroups with fuzzy orderings

76%
Huang X., Li Q.
Open Mathematics
|
2016
|
tom 14
|
nr 1
841-856
EN
The purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.
8
Content available remote

An investigation on hyperS-posets over ordered semihypergroups

76%
Tang J., Davvaz B., Xie X.-Y.
Open Mathematics
|
2017
|
tom 15
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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.
9
Content available remote

Interior and closure operators on bounded residuated lattices

64%
Rachůnek J., Svoboda Z.
Open Mathematics
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2014
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tom 12
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nr 3
534-544
EN
Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated lattices of their regular elements.
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