Results 301 to 310 of about 1,569,543 (329)
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On 1-absorbing prime ideals of commutative rings
, 2020Let R be a commutative ring with identity. In this paper, we introduce the concept of 1-absorbing prime ideals which is a generalization of prime ideals.
A. Yassine, M. Nikmehr, R. Nikandish
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On weakly 1-absorbing prime ideals
Ricerche di Matematica, 2020This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $$A\ $$ A be a commutative ring with a nonzero identity $$1\ne 0.$$ 1 ≠ 0 .
Suat Koç, Ünsal Teki̇r, E. Yıldız
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Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings
Communications in Algebra, 2020Let R be a noncommutative prime ring, I a nonzero left ideal of R, L a non-central Lie ideal of R, U the left Utumi quotient ring of R and the extended centroid of R.
B. Dhara, V. De Filippis
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Associated prime ideals over skew PBW extensions
, 2020In this article, we continue the study of ideals of the noncommutative rings of polynomial type known as skew Poincaré-Birkhoff-Witt extensions. More exactly, we focus on the associated prime ideals of these extensions.
A. Niño +2 more
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Canadian Mathematical Bulletin, 1983
AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
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AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
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Rinocchio: SNARKs for Ring Arithmetic
Journal of Cryptology, 2023C. Ganesh +2 more
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Rendiconti del Circolo Matematico di Palermo, 1993
The author proves four commutativity theorems for a prime ring \(R\) with center \(Z\) and nonzero derivation \(D\). Specifically, \(R\) is commutative if any of the following holds for all \(x\in R\): 1) \(x^ 2 D(x) - D(x)x^ 2 \in Z\) and \(\text{char }R \neq 2\); 2) \(x^ 2 D(x) -xD(x)x \in Z\) and \(\text{char }R \neq 2\); 3) \(x^ 3 D(x) = D(x)x^ 3\)
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The author proves four commutativity theorems for a prime ring \(R\) with center \(Z\) and nonzero derivation \(D\). Specifically, \(R\) is commutative if any of the following holds for all \(x\in R\): 1) \(x^ 2 D(x) - D(x)x^ 2 \in Z\) and \(\text{char }R \neq 2\); 2) \(x^ 2 D(x) -xD(x)x \in Z\) and \(\text{char }R \neq 2\); 3) \(x^ 3 D(x) = D(x)x^ 3\)
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Algebra and Logic, 1983
This paper has two types of results. First, there are proved the following theorems about rings of constants of finite dimensional \(\partial\)-Lie algebras of external derivations of rings with positive characteristic: Theorem 1. Let L be a finite-dimensional \(\partial\)-Lie algebra of external derivations of the prime ring R with positive ...
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This paper has two types of results. First, there are proved the following theorems about rings of constants of finite dimensional \(\partial\)-Lie algebras of external derivations of rings with positive characteristic: Theorem 1. Let L be a finite-dimensional \(\partial\)-Lie algebra of external derivations of the prime ring R with positive ...
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Nonlinear skew Lie derivations on prime $$*$$ ∗ -rings
Indian journal of pure and applied mathematics, 2022L. Kong, Jianhua Zhang
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1991
In commutative ring theory, three basic classes of rings are: reduced rings, integral domains, and fields. The defining conditions for these classes do not really make any use of commutativity, so by using exactly the same conditions on rings in general, we can define (and we have defined) the notions of reduced rings, domains, and division rings ...
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In commutative ring theory, three basic classes of rings are: reduced rings, integral domains, and fields. The defining conditions for these classes do not really make any use of commutativity, so by using exactly the same conditions on rings in general, we can define (and we have defined) the notions of reduced rings, domains, and division rings ...
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