Results 11 to 20 of about 300,123 (157)
On nonnil-S-Noetherian and nonnil-u-S-Noetherian rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet R be a commutative ring with identity, and let S be a multiplicative subset of R. Then R is called a nonnil-S-Noetherian ring if every nonnil ideal of R is S-finite.
Mahdou Najib +2 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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, 1970 The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms.
Holcombe, William Michael Lloyd
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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
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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
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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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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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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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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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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
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