Weakly torsion free <i>S</i>-posets

Liang, Xingliang; Laan, Valdis; Luo, Yanfeng; Khosravi, Roghaieh

doi:10.1080/00927872.2016.1236388

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…A Right S-posets can be defined analogously. Preliminary work on S-posets was carried out by Fakhruddin in the 1980s (see [4,5]) and continued in recent papers, for example, see [6][7][8][9][10][11][12][13][14]. Also see [15] for an overview.…”

Section: Introductionmentioning

confidence: 99%

A study on strongly convex hyper S-subposets in hyper S-posets

2020

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In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.

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Section: Introductionmentioning

confidence: 99%

A study on strongly convex hyper S-subposets in hyper S-posets

2020

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On a generalization of principal weak (po-)flatness of S-posets

Rashidi

Golchin

Saany

2021

Asian-European J. Math.

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In [H. Rashidi, A. Golchin and H. Mohammadzadeh saany, On [Formula: see text]-flat acts, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020) 175–197], the study of [Formula: see text]-flatness property of right acts [Formula: see text] over a monoid [Formula: see text] that can be described by means of when the functor [Formula: see text]-preserves some pullbacks is initiated. In this paper, we extend these results to [Formula: see text]-posets and present equivalent description of [Formula: see text]-po-flatness of [Formula: see text]-posets. We show that [Formula: see text]-flatness does not imply torsion freeness in [Formula: see text]-posets and give some general properties and a characterization of pomonoids for which some other properties of their posets imply this condition.

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Weakly torsion free S-posets

Cited by 2 publications

References 13 publications

A study on strongly convex hyper S-subposets in hyper S-posets

A study on strongly convex hyper S-subposets in hyper S-posets

On a generalization of principal weak (po-)flatness of S-posets

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