• Title/Summary/Keyword: precover and preenvelope

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∏-COHERENT DIMENSIONS AND ∏-COHERENT RINGS

  • Mao, Lixin
    • Journal of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.719-731
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    • 2007
  • R is called a right ${\Pi}-coherent$ ring in case every finitely generated torsion less right R-module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi}-coherent$ dimension, which measures how far away a ring is from being ${\Pi}-coherent$. This dimension has nice properties when the ring in question is coherent. In addition, we study some properties of ${\Pi}-coherent$ rings in terms of preenvelopes and precovers.

HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS

  • Yang, Gang
    • Journal of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.31-47
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    • 2012
  • The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injective dimensions at most n for some non-negative integer n. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We first consider Gorenstein at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.

Nil-COHERENT RINGS

  • Xiang, Yueming;Ouyang, Lunqun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.579-594
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    • 2014
  • Let R be a ring and $Nil_*$(R) be the prime radical of R. In this paper, we say that a ring R is left $Nil_*$-coherent if $Nil_*$(R) is coherent as a left R-module. The concept is introduced as the generalization of left J-coherent rings and semiprime rings. Some properties of $Nil_*$-coherent rings are also studied in terms of N-injective modules and N-flat modules.