Noetherian ring

This paper a Buchsbaum ring R which is not Cohen-Macaulay and we construct a Cohen-Macaulay intermediate ring A ∈ Y. In order to solve the problem, we apply the method investigated by S. Goto in 1983, L. T. Nhan and M. Brodmann 2012.

6p nguaconbaynhay12 13-06-2021 8 1   Download

In the study of abstract algebra, most of the rings that one first encounters are rings with Invariant Basis Number property. This class of rings includes all nonzero commutative rings and (left) Noetherian rings.

8p nguaconbaynhay11 07-04-2021 15 2   Download

In this paper we introduce the notion of bounded modules and fully bounded modules. A right R-module M is called a bounded module if every essential submodule of M contains a fully invariant submodule of M which is essential in MR. A module M is called a fully bounded module if M/X is bounded for any prime submodule X of M.

7p nguaconbaynhay11 07-04-2021 11 2   Download

In this paper, we prove that the Gorensteiness, the injective resolution, the injective envelope and Gorenstein dimension of modules are preserved by specializations.

6p tamynhan8 04-11-2020 11 1   Download

In this paper, cyclic c−injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic c−injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.

10p danhdanh27 07-01-2019 10 1   Download

Uniqueness properties of coprimary decompositions of modules over non-commutative rings are presented. In this paper, by making use of the technique employed, we shall prove uniqueness properties of coprimary decompositions.

12p danhdanh27 07-01-2019 13 1   Download

In this paper we characterize Q-modules and almost Q-modules. Next we estblish some equivalent conditions for an almost Q-module to be a Q-module. Using these results, some characterizations are given for Noetherian Q-modules.

11p danhdanh27 07-01-2019 24 3   Download

This paper we study the augmented graded Noetherian modules and try to give some relationships between the Noetherian modules in the category R − Agr and the Noetherian modules in the category Re − gr.

6p tuongvidanh 06-01-2019 37 1   Download

Let (R, m) be a noetherian local ring and M a finitely generated Rmodule. In this paper, we study the number of elements in a minimal system of generators of the homogeneous ideal in the idealization ring RnM. As immediate consequences, we presented a characterization for RnM being a regular local ring and homogeneous ideals of RnM being parameters ideals.

5p tonymina21 05-12-2018 34 1   Download

Let (R, m) be a Noetherian local ring and M a finitely generated R-module of dimension d. Let x = (x1, . . . , xd) be a system of parameters of M. In this paper, we give some applications of dd-sequences in the study of certain Koszul homology modules. Recall that the notion of dd-sequence was introduced by N. T. Cuong and D. T. Cuong [4], which is a distinguished type of d-sequence defined by C. Huneke.

6p blackwidow123 15-06-2018 16 2   Download

There are notes of course of lectures on Field theory aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. These lectures were preceded by an elementary course on group theory, vector spaces and ideal theory of rings—especially of Noetherian rings. A knowledge of these is presupposed in these notes.

0p nunongnuna 01-04-2013 72 15   Download

We prove Maruyama’s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of finite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant.

27p tuanloccuoi 04-01-2013 49 8   Download

Let (R, m) be a commutative Noetherian local ring the maximal ideal and A an Artinian R-module with Ndim A = d. For each system of parameters x (x1 , ..., xd ) of A, we denote by e(x, A) the multipility of A with respect to x. Let n (n1 , n2 , ..., nd ) be a d-tuple of positive integers. The paper concerns to the function d-variables I(x(n); A) := where

11p tuanlocmuido 19-12-2012 33 1   Download

It is shown that: (1) Let R be a simple right Noetherian ring, then the following conditions are equivalent: (i) R is a right SI ring; (ii) Every cyclic singular right R - module is pseudo - injective. (2) Let R be a right artinian ring such that every finite generated right R - module is a direct sum of a projective module and a pseudo - injective module. Then: (i) R/Soc(RR ) is a semisimple artinian ring; (ii) J (R) ⊂ Soc(RR ); (iii) J 2 (R) = 0. (3) Let R be a ring with condition (∗ ),...

5p tuanlocmuido 19-12-2012 41 2   Download