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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Format: | Article |
Language: | English |
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Shahid Beheshti University
2018-01-01
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Series: | Categories and General Algebraic Structures with Applications |
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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. |
first_indexed | 2024-12-16T16:24:31Z |
format | Article |
id | doaj.art-2ead047ee9104d298f33d68b12a76f0b |
institution | Directory Open Access Journal |
issn | 2345-5853 2345-5861 |
language | English |
last_indexed | 2024-12-16T16:24:31Z |
publishDate | 2018-01-01 |
publisher | Shahid Beheshti University |
record_format | Article |
series | Categories and General Algebraic Structures with Applications |
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 |
work_keys_str_mv | AT roghaiehkhosravi onpotorsionfreeandprincipallyweaklypoflatsposets AT xingliangliang onpotorsionfreeandprincipallyweaklypoflatsposets |