Results 21 to 30 of about 1,487 (222)
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 ...
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Noetherian properties in composite generalized power series rings
Open Mathematics, 2020 Let (Γ,≤)({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let Γ⁎=Γ\{0}{{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\}. Let D⊆ED\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ...
Lim Jung Wook, Oh Dong Yeol
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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 +1 more
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Left Noetherian rings with differentially trivial proper quotient rings
Karpatsʹkì Matematičnì Publìkacìï, 2012 We characterize left Noetherian rings with differentially trivial proper quotient rings.
O. D. Artemovych
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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
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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
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International Journal of Computational Intelligence Systems, 2020 In this paper, by considering the notion of MV-modules, which is the structure that naturally correspond to lu-modules over lu-rings, we investigate some properties of a new kind of MV-modules, that we introduced in Borzooei and Saidi Goraghani, Free MV ...
S. Saidi Goraghani +3 more
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TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES [PDF]
Journal of Algebraic Systems, 2021 Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then ...
A. R. Nazari, F. Rastgoo
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Essentially iso-retractable modules and rings
Karpatsʹkì Matematičnì Publìkacìï, 2022 A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V ...
A.K. Chaturvedi +3 more
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Some properties of graded generalized 2-absorbing submodules
Demonstratio Mathematica, 2022 Let GG be an abelian group with identity ee. Let RR be a GG-graded commutative ring and MM a graded RR-module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components.
Alghueiri Shatha, Al-Zoubi Khaldoun
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