On (po-)torsion free and principally weakly (po-)flat $S$-posets

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct...

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Main Authors: Roghaieh Khosravi, Xingliang Liang
Format: Article
Language:English
Published: Shahid Beheshti University 2018-01-01
Series:Categories and General Algebraic Structures with Applications
Subjects:
Online Access:http://www.cgasa.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf
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author Roghaieh Khosravi
Xingliang Liang
author_facet Roghaieh Khosravi
Xingliang Liang
author_sort Roghaieh Khosravi
collection DOAJ
description In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are weakly po-flat.
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spelling doaj.art-2ead047ee9104d298f33d68b12a76f0b2022-12-21T22:24:49ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612018-01-0181354944578On (po-)torsion free and principally weakly (po-)flat $S$-posetsRoghaieh Khosravi0Xingliang Liang1Department of Mathematics, Fasa University, Fasa, P.O. Box 74617- 81189, IranDepartment of mathematics, Shaanxi University of Science and Technology, Shaanxi, P.O. Box 710021, ChinaIn this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are weakly po-flat.http://www.cgasa.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdfTorsion freepo-torsion freeprincipally weakly flatpomonoid$S$-poset
spellingShingle Roghaieh Khosravi
Xingliang Liang
On (po-)torsion free and principally weakly (po-)flat $S$-posets
Categories and General Algebraic Structures with Applications
Torsion free
po-torsion free
principally weakly flat
pomonoid
$S$-poset
title On (po-)torsion free and principally weakly (po-)flat $S$-posets
title_full On (po-)torsion free and principally weakly (po-)flat $S$-posets
title_fullStr On (po-)torsion free and principally weakly (po-)flat $S$-posets
title_full_unstemmed On (po-)torsion free and principally weakly (po-)flat $S$-posets
title_short On (po-)torsion free and principally weakly (po-)flat $S$-posets
title_sort on po torsion free and principally weakly po flat s posets
topic Torsion free
po-torsion free
principally weakly flat
pomonoid
$S$-poset
url http://www.cgasa.ir/article_44578_81b18d36c9840fe2d5160c1baf42be5a.pdf
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