Results 21 to 30 of about 252 (184)

Bi-artinian noetherian rings [PDF]

Glasgow Mathematical Journal, 2001
A noetherian ring R satisfies the descending chain condition on two-sided ideals (“is bi-artinian”) if and only if, for each prime P ∈ spec(R), R/P has a unique minimal ideal (necessarily idempotent and left-right essential in R/P). The analogous statement for merely right noetherian rings is false, although our proof does not use the full ...
openaire   +2 more sources

Subrings of Noetherian rings [PDF]

Proceedings of the American Mathematical Society, 1974
Let S S be a subring of a ring R R such that R R is a finitely generated right S S -module. Clearly, if S S is a right Noetherian ring then so is R R . Generalizing a result of P. M.
Formanek, Edward, Jategaonkar, Arun Vinayak   +1 more
openaire   +2 more sources

On Noetherian prime rings [PDF]

Transactions of the American Mathematical Society, 1965
Classical left quotient rings are defined symmetrically. R is right (resp. left) quotient-simple in case R has a classical right (resp. left) quotient ring S which is isomorphic to a complete ring Dn of n X n matrices over a (not necessarily commutative) field D. R is quotient-simple if R is both left and right quotient-simple.
Faith, Carl, Utumi, Yuzo
openaire   +2 more sources

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

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

MONOLITHIC MODULES OVER NOETHERIAN RINGS [PDF]

Glasgow Mathematical Journal, 2011
AbstractWe study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantised Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained by Carvalho et al. (Carvalho et al., Injective modules over down-up algebras, Glasgow Math. J. 52A (2010), 53–59) for down-up algebras.
Carvalho, Paula A. A. B., Musson, Ian M.
openaire   +3 more sources

Pythagorean fuzzy Artinian and Noetherian ring [PDF]

Computational Algorithms and Numerical Dimensions
The 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, Idris Bakhadach, Sofyane Achik, Hamid Sadiki   +3 more
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

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