Bull. Korean Math. Soc. 2002; 39(4): 577-587
Printed December 1, 2002
Copyright © The Korean Mathematical Society.
Mohamad Hosin Bijan-Zadeh and S. Rasoulyar
University For Teacher Education, University For Teacher Education
Let $A$ be a commutative ring and $M$ an Artinian $A$-module. Let $\sigma$ be a torsion radical functor and $(T,F)$ it's corresponding partition of $\Spec(A)$. In [1] the concept of Cohen-Macauly modules was generalized. In this paper we shall define $\sigma$-co-Cohen-Macaulay (abbr. $\sigma$-co-CM). Indeed this is one of the aims of this paper, we obtain some satisfactory properties of such modules. Another aim of this paper is to generalize the concept of cograde by using the left derived functor $U_i^{\fa}(-)$ of the $\fa$-adic completion functor, where $\fa$ is contained in Jacobson radical of $A$.
Keywords: torsion theory, co-Cohen-Macaulay, local homology modules, Krull dimension, cograde
MSC numbers: 13C99, 13D30, 13E10
2020; 57(5): 1165-1176
2018; 55(2): 625-631
2016; 53(1): 153-161
2004; 41(2): 387-391
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd