Results 21 to 30 of about 2,266 (207)
On multiplication $fs$-modules and dimension symmetry [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian.
Nasrin Shirali +2 more
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
Projective prime ideals and localisation in pi-rings [PDF]
, 2001 The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following. THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PR is projective. Then P is left localisable and RP is
Chatters, A. W. +5 more
core +1 more source
On Noetherianness of Nash rings [PDF]
Proceedings of the American Mathematical Society, 1984 We introduce a class of rings, called Nash Rings, which generalize the notation of rings of Nash functions. Let k k be any field, X X be a normal algebraic variety in k n {k^n} , and U ⊂ X U \subset X .
Mora, Fulvio, Raimondo, Mario
openaire +1 more source
On Semiprime Noetherian PI-Rings [PDF]
, 2000 Let R be a semiprime Noetherian PI-ring and Q(R) the semisimple Artinian ring of fractions of R. We shall prove the following conditions are equivalent: (1) the Krull dimention of R is at most one, (2) Any ring between R and Q(R) is again right ...
Chiba, Katsuo
core +1 more source
On the Ring of Quotients of a Noetherian Ring [PDF]
Canadian Mathematical Bulletin, 1965 This paper is largely an expository account of known facts, but it contains at least one result believed to be new, Proposition 6.Our main technique is the method of lifting idempotents developed in Part I. This has been treated in the literature, but not quite in the generality required here.
openaire +1 more source
Upper Cohen-Macaulay Dimension [PDF]
, 2004 In this paper, we define a homological invariant for finitely generated modules over a commutative noetherian local ring, which we call upper Cohen-Macaulay dimension.
Tokuji Araya +5 more
core +1 more source
A theorem on Noetherian hereditary rings [PDF]
Pacific Journal of Mathematics, 1973 It is shown (Theorem 2) that a semi-prime, left noetherian, left hereditary, two-sided Goldie ring is right noetherian if and only if the right module (Q/R) φ R contains a copy of every simple right iέ-module, where Q is the classical quotient ring of R.
Camillo, Victor P., Cozzens, J.
openaire +3 more sources
, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
core +1 more source
When Are Graded Rings Graded S-Noetherian Rings
Mathematics, 2020 Let Γ be a commutative monoid, R=⨁α∈ΓRα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian
Dong Kyu Kim, Jung Wook Lim
doaj +1 more source