Factorizations of automorphism groups of finitely generated module over a commutative ring. II

1990 ◽  
Vol 42 (9) ◽  
pp. 1106-1113
Author(s):  
N. S. Chernikov
Keyword(s):  
Commutative Ring ◽  
Automorphism Groups ◽  
Finitely Generated ◽  
Finitely Generated Module

scholarly journals Inertial subalgebras of algebras possessing finite automorphism groups

1979 ◽  
Vol 28 (3) ◽  
pp. 335-345 ◽  
Author(s):  
Nicholas S. Ford
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Jacobson Radical ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Fixed Ring ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.

Artinian modules over commutative rings

1992 ◽  
Vol 111 (1) ◽  
pp. 25-33 ◽  
Author(s):  
R. Y. Sharp
Keyword(s):  
Commutative Ring ◽  
Local Ring ◽  
Commutative Rings ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Artinian Modules ◽  
Noetherian Local Ring ◽  
Matlis Duality ◽  
Artinian Module

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring R (throughout the paper, R will denote a commutative ring with identity) can, for some purposes at least, be reduced to the study of an Artinian module A' over a complete (Noetherian) local ring; in the latter situation, Matlis' duality 1 (alternatively, see 6, ch. 5) is available, and this means that the investigation can often be converted into a dual one about a finitely generated module over a complete (Noetherian) local ring.

A SUBMODULE UNRELATED TO THE CORRESPONDING FACTOR MODULE OVER A COMMUTATIVE RING

2003 ◽  
Vol 02 (01) ◽  
pp. 101-104 ◽  
Author(s):  
YASUTAKA SHINDOH
Keyword(s):  
Commutative Ring ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Factor Module

In this paper we introduce a new concept "unrelated pairs". Using this concept, we study a relation between homomorphisms and direct summands of a finitely generated module.

scholarly journals The asymptotic closure of an ideal relative to a module

2001 ◽  
Vol 32 (3) ◽  
pp. 231-235
Author(s):  
Sylvia M. Foster ◽  
Johnny A. Johnson
Keyword(s):  
Commutative Ring ◽  
Integral Closure ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Noetherian Module ◽  
The Ideal

In this paper we introduce the concept of the asymptotic closure of an ideal of a commutative ring $ R $ with identity relative to a unitary $ R $-module $ M $. This work extends results from P. Samuel, M. Nagata, J. W. Petro and Sharp, Tiras, and Yassi. Our objectives in this paper are to establish the cancellation law for the asymptotic completion of an ideal relative to a finitely generated module and show that the integral closure of an ideal relative to a Noetherian module $ M $ coincides with the asymptotic closure of the ideal relative to the Noetherian module $ M $.

scholarly journals NOETHERIAN SPECTRUM ON RINGS AND MODULES

2011 ◽  
Vol 53 (3) ◽  
pp. 707-715
Author(s):  
DAVID E. RUSH
Keyword(s):  
Commutative Ring ◽  
Symmetric Algebra ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Prime Submodules ◽  
Noetherian Property ◽  
Carry Over

AbstractIt is shown that the well-known characterizations of when a commutative ringRhas Noetherian spectrum carry over to characterizations of when the set Spec(M) of prime submodules of a finitely generated moduleMis Noetherian. The symmetric algebraSR(M) ofMis used to show that the Noetherian property of Spec(R), and some related properties, pass from the ringRto the finitely generatedR-modules.

On a Class of Automaton Algebras

2016 ◽  
Vol 60 (1) ◽  
pp. 31-38 ◽  
Author(s):  
Ferran Cedó ◽  
Jan Okniński
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Module ◽  
Commutative Subalgebra

AbstractWe show that every finitely generated algebra that is a finitely generated module over a finitely generated commutative subalgebra is an automaton algebra in the sense of Ufnarovskii.

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.

Prime uniserial modules and rings

2019 ◽  
Vol 18 (02) ◽  
pp. 1950035 ◽  
Author(s):  
M. Behboodi ◽  
Z. Fazelpour
Keyword(s):  
Commutative Rings ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Direct Sum ◽  
Dedekind Domains ◽  
Prime Submodules ◽  
Uniserial Modules ◽  
Structure Formula

We define prime uniserial modules as a generalization of uniserial modules. We say that an [Formula: see text]-module [Formula: see text] is prime uniserial ([Formula: see text]-uniserial) if its prime submodules are linearly ordered by inclusion, and we say that [Formula: see text] is prime serial ([Formula: see text]-serial) if it is a direct sum of [Formula: see text]-uniserial modules. The goal of this paper is to study [Formula: see text]-serial modules over commutative rings. First, we study the structure [Formula: see text]-serial modules over almost perfect domains and then we determine the structure of [Formula: see text]-serial modules over Dedekind domains. Moreover, we discuss the following natural questions: “Which rings have the property that every module is [Formula: see text]-serial?” and “Which rings have the property that every finitely generated module is [Formula: see text]-serial?”.

Primary ideals with finitely generated radical in a commutative ring

1993 ◽  
Vol 78 (1) ◽  
pp. 201-221 ◽  
Author(s):  
Robert Gilmer ◽  
William Heinzer
Keyword(s):  
Commutative Ring ◽  
Finitely Generated ◽  
Primary Ideals
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