Gröbner Basis and Indecomposable Modules over a like Dedekind Ring
نویسنده
چکیده
Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.
منابع مشابه
Computing the Additive Structure of Indecomposable Modules over Dedekind-like Rings Using Gröbner Bases
We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M . This algorithm is based on Gröbner bases theory. We apply this method to determine the additive structure of indecomposable modules over the following Dedeking-like rings: ZCp, where Cp is the cyclic group of order a prime p, and the p−pullback {Z→ Zp ← Z} of Z⊕ Z.
متن کاملCzechoslovak Mathematical Journal
First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if R is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime R-modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
متن کاملON COMULTIPLICATION AND R-MULTIPLICATION MODULES
We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...
متن کاملBig Indecomposable Modules and Direct-sum Relations
The main theorem of this paper complements the tame-wild dichotomy for commutative Noetherian rings, obtained by Klingler and Levy [14]–[16]. They gave a complete classification of all finitely generated modules over Dedekind-like rings (cf. Definition 1.1) and showed that, over any ring that is not a homomorphic image of a Dedekind-like ring, the category of finite-length modules has wild repr...
متن کاملϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...
متن کامل