• 제목/요약/키워드: P-coherent ring

검색결과 3건 처리시간 0.014초

WHEN IS AN ENDOMORPHISM RING P-COHERENT?

  • Mao, Lixin
    • 대한수학회지
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    • 제46권1호
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    • pp.99-111
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    • 2009
  • A ring is called left P-coherent if every principal left ideal is finitely presented. Let M be a right R-module with the endomorphism ring S. We mainly study the P-coherence of S. It is shown that S is a left P-coherent ring if and only if the left annihilator $ann_S$(X) is a finitely generated left ideal of S for any M-cyclic submodule X of M if and only if every cyclically M-presented right R-module has an M-torsionfree preenvelope. As applications, we investigate when the endomorphism ring S is left PP or von Neumann regular.

ON ALMOST QUASI-COHERENT RINGS AND ALMOST VON NEUMANN RINGS

  • El Alaoui, Haitham;El Maalmi, Mourad;Mouanis, Hakima
    • 대한수학회보
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    • 제59권5호
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    • pp.1177-1190
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    • 2022
  • Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α1, …, αp and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and AnnRm) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αn, bn) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES

  • Zeng, Yuedi;Chen, Jianlong
    • 대한수학회보
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    • 제50권1호
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    • pp.11-24
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    • 2013
  • Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($m$, $n$)-injective if $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(N, P) = 0 for any ($m$, $n$)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.