Strongly Ƥ-projective Modules and Ƥ-projective Complexes
International Journal of Theoretical and Applied Mathematics
Volume 5, Issue 6, December 2019, Pages: 118-124
Received: Oct. 30, 2019; Accepted: Nov. 26, 2019; Published: Dec. 19, 2019
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Author
Liang Yan, College of Mathematics and Physics Science, Hunan University of Arts and Science, Changde, P. R. China
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Abstract
In this paper we first study the properties of Strongly Ƥ-projective modules, and obtain some equivalent conclusions about Strongly Ƥ-projective modules, it is proved that a finitely generated right R-module N is strongly Ƥ-projective if and only if Exti (N, R) = 0 for all i ≥ 1 over left noetherian and right perfect ring, a Ƥ-projective right R-module N is strongly Ƥ-projective if and only if the first syzygy of N is strongly Ƥ-projective. Then we extend the notion of Ƥ-projective modules to that of Ƥ-projective complexes. We study the relationships between Ƥ-projective complexes and Ƥ-projective modules, it is proved that a complex C is Ƥ-projective if and only if every Ci is Ƥ-projective for every integer i if and only if Ext1 (C, P) = 0 for every projective complex Ƥ if and only if for every exact sequence 0→AƤC→0 with Ƥ projective, A→Ƥ is a projective preenvelope of A. Some characterizations of Ƥ-projective complexes also obtained.
Keywords
Strongly Ƥ-projective Module, Ƥ-projective Module, Ƥ-projective Complex
To cite this article
Liang Yan, Strongly Ƥ-projective Modules and Ƥ-projective Complexes, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 6, 2019, pp. 118-124. doi: 10.11648/j.ijtam.20190506.16
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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