Results 21 to 30 of about 263 (184)
Some results on PIT and GPIT theorems [PDF]
Journal of Hyperstructures, 2016 In this paper we generalize the P IT and the GP IT that can be used to study the heights of prime ideals in a general commutative Noetherian ring R and the dimension theory of such a ring and we use these generalizations to prove some useful results.
M. Ebrahimpour
doaj +1 more source
FALTINGS’ LOCAL-GLOBAL PRINCIPLE FOR THE MINIMAXNESS OF LOCAL COHOMOLOGY MODULES DEFINED BY A SYSTEM OF IDEALS [PDF]
Journal of Algebraic Systems, 2023 Let R be a commutative Noetherian ring with nonzero identity. Let φ be a system of ideals of R and let M, N two finitely generated R-modules. We prove that there are local- global principles for the finiteness and minimaxness of generalized local ...
F. Dehghani-Zadeh, A.R. Hajikarimi
doaj +1 more source
Homological Dimension in Noetherian Rings. [PDF]
Transactions of the American Mathematical Society, 1956 Introduction. Throughout this paper it is assumed that all rings are commutative, noetherian rings with unit element and all modules are unitary. The major purpose of this paper is to extend to arbitrary noetherian rings the homological invariants which were introduced in [2] for local rings.
Auslander, Maurice, Buchsbaum, David A.
openaire +4 more sources
Canadian Mathematical Bulletin, 1976 In the latter part of the 1950’s some interesting papers appeared (e.g. [2] and [10]) which examined the relationships occurring between the purely algebraic and homological aspects of the theory of finitely generated modules over Noetherian rings. Many of these relationships remain valid if one considers the much wider class of rings determined by the
openaire +2 more sources
ANNIHILATOR OF LOCAL COHOMOLOGY MODULES UNDER THE RING EXTENSION R⊂R[X] [PDF]
Journal of Algebraic Systems, 2020 Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]).
M. Seidali Samani, K. Bahmanpour
doaj +1 more source
Pythagorean fuzzy Artinian and Noetherian ring [PDF]
Computational Algorithms and Numerical DimensionsThe Pythagorean fuzzy set is acknowledged for its proficiency in managing uncertainty across multifarious domains. In this investigation, we advance the Pythagorean fuzzy Artinian ring as an evolutionary progression from the conventional fuzzy ring ...
Meryem Fakhraoui +3 more
doaj +1 more source
Trivial Extension of π-Regular Rings [PDF]
Engineering and Technology Journal, 2016 In this paper we investigate if it is possible that the trivial extension ring T(R,R) inherit the properties of the ring R and present the relationship between the trivial extension T(R,M) of a ring R by an R-module M and theπ-regularity of Rby taking ...
Areej M. Abduldaim
doaj +1 more source
On the properties of weak CM rings
上海师范大学学报. 自然科学版, 2022 In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology ...
XUE Wensi, ZHOU Caijun
doaj +1 more source
Co-Cohen-Macaulay Modules and Local Cohomology
Journal of Mathematics, 2013 Let be a commutative Noetherian local ring and let be a finitely generated -module of dimension . Then the following statements hold: (a) if width for all with , then is co-Cohen-Macaulay of Noetherian dimension ; (b) if is an unmixed -module and ...
Hero Saremi, Amir Mafi
doaj +1 more source
Rings Graded By a Generalized Group
Topological Algebra and its Applications, 2014 The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
doaj +1 more source