Results 11 to 20 of about 1,487 (222)
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
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Mathematics, 2020 Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite.
Min Jae Kwon, Jung Wook Lim
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Quaestiones Mathematicae, 2023 Let $R$ be a ring and $S$ a multiplicative subset of $R$. Then $R$ is called a uniformly $S$-Noetherian ($u$-$S$-Noetherian for abbreviation) ring provided there exists an element $s\in S$ such that for any ideal $I$ of $R$, $sI \subseteq K$ for some finitely generated sub-ideal $K$ of $I$.
Chen, Mingzhao +4 more
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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
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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
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Abnormalities in Noetherian Rings [PDF]
Proceedings of the American Mathematical Society, 1979 If P ⊆ Q P \subseteq Q are prime ideals in some ring R and if rank Q = rank ( Q / P ) + rank P + k Q = {\text {rank}}(Q/P) + {\text {rank}}\;P + k , then
Arnold, J. T., Boisen, M. B. jun.
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On stable noetherian rings [PDF]
Transactions of the American Mathematical Society, 1975 A ring R is called stable if every localizing subcategory of R M _R{\text {M}} is closed under taking injective envelopes. In this paper the stable noetherian rings are characterized in terms of the idempotent kernel functors of R
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Locally Noetherian Commutative Rings [PDF]
Transactions of the American Mathematical Society, 1971 This paper centers around the theorem that a commutative ring R R is noetherian if every R P , P {R_P},P prime, is noetherian and every finitely generated ideal of R R has only finitely many weak-Bourbaki associated primes. A more
Heinzer, William, Ohm, Jack
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Chain conditions on composite Hurwitz series rings
Open Mathematics, 2017 In this paper, we study chain conditions on composite Hurwitz series rings and composite Hurwitz polynomial rings. More precisely, we characterize when composite Hurwitz series rings and composite Hurwitz polynomial rings are Noetherian, S-Noetherian or ...
Lim Jung Wook, Oh Dong Yeol
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On the regulator problem for linear systems over rings and algebras
Open Mathematics, 2021 The regulator problem is solvable for a linear dynamical system Σ\Sigma if and only if Σ\Sigma is both pole assignable and state estimable. In this case, Σ\Sigma is a canonical system (i.e., reachable and observable).
Hermida-Alonso José Ángel +3 more
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