Yazar "Argac, N" seçeneğine göre listele

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    Derivations, products of derivations, and commutativity in near-rings
    (World Scientific Publ Co Pte Ltd, 2001) Bell, HE; Argac, N
    For a zero-symmetric 3-prime near-ring N, we study three kinds of conditions: (a) conditions involving two derivations d(1), d(2) which imply that d(1) = 0 or d(2) = 0; (b) conditions involving derivations which force (N, +) to be abelian or N to be a commutative ring; (c) the condition that d(n)(S) is multiplicatively central for some derivation d and subset S of N.
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    Lie Ideals and Symmetrical Bi-Derivations of Prime-Rings
    (Plenum Press Div Plenum Publishing Corp, 1993) Argac, N; Yenigul, Ms; Gruber, B
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    On centroid and extended centroid of rings
    (Marcel Dekker Inc, 2003) Argac, N; Ponomarev, KN
    We apply a notion of extended centroid to the whole class of nonassociative rings. We investigate the relation between the centroid and the extended centroid of a nonassociative ring.
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    On centroid and extended centroid of rings
    (Marcel Dekker Inc, 2003) Argac, N; Ponomarev, KN
    We apply a notion of extended centroid to the whole class of nonassociative rings. We investigate the relation between the centroid and the extended centroid of a nonassociative ring.
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    On prime and semiprime rings with derivations
    (World Scientific Publ Co Pte Ltd, 2006) Argac, N
    Let R be a ring and S a nonempty subset of R. A mapping f : R --> R is called commuting on S if [f (x), x] = 0 for all x is an element of S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is commuting on I if one of the following conditions holds: (i) For all x, y is an element of I, either d([x, y]) = [x, y] or d([x, y]) = - [x, y]. (ii) For all x, y is an element of I, either d(x circle y) = x circle y or d(x circle y) = - (x circle y). (iii) R is 2-torsion free, and for all x, Y is an element of I, either [d(x), d(y)] = d([x, y]) or [d(x), d(y)] = d([y, x]). Furthermore, if d(I) not equal {0}, then R has a nonzero central ideal. Finally, we introduce the notation of generalized biderivation and prove that every generalized biderivation. on a noncommutative prime ring is a biderivation.
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    Some results on derivations in nearrings
    (Springer, 2001) Argac, N; Bell, HE; Fong, Y; Maxson, C; Meldrum, J; Pilz, G; VanderWalt, A; VanWyk, L
    Let N denote a 3-prime near-ring. We prove that if 2N not equal {0} and d(1) and d(2) are nonzero derivations on N. then d(1) d(2) cannot act as a derivation on a nonzero additively-closed semigroup ideal. We then establish some results involving conditions of form d(x)f(x) = 0, where d is a derivation on N and f is an endomorphism of N.
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    Weakly and strongly regular near-rings
    (World Scientific Publ Co Pte Ltd, 2005) Argac, N; Groenewald, NJ
    In this paper, we prove some basic properties of left weakly regular near-rings. We give an affirmative answer to the question whether a left weakly regular near-ring with left unity and satisfying the IFP is also right weakly regular. In the last section, we use among others left 0-prime and left completely prime ideals to characterize strongly regular near-rings.