scholarly journals Finitely Generated Modules over Group Rings of a Direct Product of Two Cyclic Groups

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ahmed Najim ◽  
Mohammed Elhassani Charkani
Keyword(s):  
Direct Product ◽  
Simple Form ◽  
Group Rings ◽  
Finitely Generated ◽  
Commutative Field ◽  
Cyclic Groups ◽  
Finitely Generated Modules

Let K be a commutative field of characteristic p>0 and let G=G1×G2, where G1 and G2 are two finite cyclic groups. We give some structure results of finitely generated K[G]-modules in the case where the order of G is divisible by p. Extensions of modules are also investigated. Based on these extensions and in the same previous case, we show that K[G]-modules satisfying some conditions have a fairly simple form.

scholarly journals Warfield p-Invariants in Abelian Group Rings of Characteristic p

2013 ◽  
Vol 31 (2) ◽  
pp. 183
Author(s):  
Peter Danchev
Keyword(s):  
Abelian Group ◽  
Direct Product ◽  
Group Ring ◽  
General Strategy ◽  
Group Rings ◽  
Finitely Generated ◽  
Characteristic P ◽  
Commutative Group Ring ◽  
Normalized Units ◽  
Finite Direct Product

We calculate Warfield p-invariants Wα,p(V (RG)) of the group of normalized units V (RG) in a commutative group ring RG of prime char(RG) = p in each of the following cases: (1) G0/Gp is finite and R is an arbitrary direct product of indecomposable rings; (2) G0/Gp is bounded and R is a finite direct product of fields; (3) id(R) is finite (in particular, R is finitely generated). Moreover, we give a general strategy for the computation of the above Warfield p-invariants under some restrictions on R and G. We also point out an essential incorrectness in a recent paper due to Mollov and Nachev in Commun. Algebra (2011).

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

scholarly journals Higher K -theory of group-rings of virtually infinite cyclic groups

2003 ◽  
Vol 325 (4) ◽  
pp. 711-726 ◽  
Author(s):  
Aderemi O. Kuku ◽  
Guoping Tang
Keyword(s):  
Group Rings ◽  
Cyclic Groups ◽  
K Theory

Finitely generated modules over valuation rings

1984 ◽  
Vol 12 (15) ◽  
pp. 1795-1812 ◽  
Author(s):  
Luigi Salce ◽  
Paolo Zanardo
Keyword(s):  
Finitely Generated ◽  
Valuation Rings ◽  
Finitely Generated Modules

scholarly journals Maximal depth property of finitely generated modules

2018 ◽  
Vol 17 (11) ◽  
pp. 1850202 ◽  
Author(s):  
Ahad Rahimi
Keyword(s):  
Local Ring ◽  
Finitely Generated ◽  
Noetherian Local Ring ◽  
Maximal Depth ◽  
Finitely Generated Modules ◽  
Associated Prime

Let [Formula: see text] be a Noetherian local ring and [Formula: see text] a finitely generated [Formula: see text]-module. We say [Formula: see text] has maximal depth if there is an associated prime [Formula: see text] of [Formula: see text] such that depth [Formula: see text]. In this paper, we study finitely generated modules with maximal depth. It is shown that the maximal depth property is preserved under some important module operations. Generalized Cohen–Macaulay modules with maximal depth are classified. Finally, the attached primes of [Formula: see text] are considered for [Formula: see text].

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