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Representations of prime rings [PDF]
Transactions of the American Mathematical Society, 1953 This paper is a continuation of the study of prime rings started in [2]. We recall that a prime ring is a ring having its zero ideal as a prime ideal. A right (left) ideal I of a prime ring R is called prime if abCI implies that acI (bCI), a and b right (left) ideals of R with b5O (aXO).
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Derivations in Prime Rings [PDF]
Proceedings of the American Mathematical Society, 1982 Let R R be a ring and d ≠ 0 d \ne 0 a derivation of R R such that d ( x n ) = 0 d({x^n}) = 0 , n = n ( x ) ⩾ 1
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Smarandache Completely Semi Prime Ideal With Respect To An Element Of A Near Ring
Journal of Kufa for Mathematics and Computer, 2014 In this paper ,we introduce the notions of smarandache completely semi prime ideal (S.C.S.P.I),and smarandache completely semi prime ideal with respect to an element x of a near ring N denoted by (x-S.C.S.P.I) , and smarandache ...
Hussien Hadi Abass +1 more
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On Cohen-Macaulayness and depth of ideals in invariant rings [PDF]
, 2015 We investigate the presence of Cohen-Macaulay ideals in invariant rings and show that an ideal of an invariant ring corresponding to a modular representation of a $p$-group is not Cohen-Macaulay unless the invariant ring itself is.
Kohls, Martin, Sezer, Müfit
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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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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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International Journal of Mathematics and Mathematical Sciences, 1997 Let R be a prime ring of characteristic not 2, U a nonzero ideal of R and 0≠da(α,β)-derivation of R where α and β are automorphisms of R. i) [d(U),a]=0 then a∈Z ii) For a,b∈R, the following conditions are equivalent (I) α(a)d(x)=d(x)β(b), for all x∈U ...
Neşet Aydin
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On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings
مجلة بغداد للعلوم, 2016 Let R be a ?-ring, and ?, ? be two automorphisms of R. An additive mapping d from a ?-ring R into itself is called a (?,?)-derivation on R if d(a?b) = d(a)? ?(b) + ?(a)?d(b), holds for all a,b ?R and ???. d is called strong commutativity preserving (SCP)
Baghdad Science Journal
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Completely Semi Prime Ideal With Respect To An Element Of A Near Ring
Journal of Kufa for Mathematics and Computer, 2011       In this paper ,we introduce the notions of completely semi prime ideal with respect to an element x (x-C.S.P.I) of a near ring and the completely semi prime ideal near ring with respect to an element x (x-C.S.P.I ) . 1.
Hussien Hadi Abass +1 more
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