Results 31 to 40 of about 204,704 (282)
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. +2 more
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Derivations in Prime Rings [PDF]
Proceedings of the American Mathematical Society, 1957 We prove two theorems that are easily conjectured, namely: (1) In a prime ring of characteristics not 2, if the iterate of two derivations is a derivation, then one of them is zero; (2) If d is a derivation of a prime ring such that, for all elements a of the ring, ad(a) -d(a)a is central, then either the ring is commutative or d is zero. DEFINITION. A
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The Prime Spectra of Regular Rings [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2007 In this work, we study the prime spectrum of regular rings. Also we study some topological concepts as quasi-compact, compact, totally disconnected, and irreducible topological space in order to prove some new results on the prime spectrum of regular ...
Nazar Shuker +2 more
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About unital and non-unital duo rings [PDF]
Proceedings of the Estonian Academy of SciencesSeveral results about one-sided duo rings and duo rings are generalized from the case of unital rings to the case of arbitrary associative rings in this paper.
Mart Abel, Eva-Lotta Elmanovitš
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A one-sided Prime Ideal Principle for noncommutative rings
, 2011 Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals ...
Andrunakievich V. A. +7 more
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Proceedings of the Edinburgh Mathematical Society, 1991 A ring R is prime essential if R is semiprime and for each prime ideal P of R, P ∩ I ≠0 whenever I is a nonzero two-sided ideal of R. Examples of prime essential rings include rings of continuous functions and infinite products modulo infinite sums. We show that the class of prime essential rings is closed under many familiar operations; in particular,
Gardner, B. J., Stewart, P. N.
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A prime ideal principle for two-sided ideals
, 2016 Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the Prime Ideal ...
Reyes, Manuel L.
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International Journal of Mathematics and Mathematical Sciences, 1994 Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of ...
Hazar Abu-Khuzam, Adil Yaqub
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Derivation Requirements on Prime Near-Rings for Commutative Rings
Jurnal Ilmu Dasar, 2019 Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative ...
Dian Winda Setyawati +2 more
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Jordan left (?,?) -derivations Of ?-prime rings
مجلة بغداد للعلوم, 2011 It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.
Baghdad Science Journal
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