Yazar "Aydin, Neşet" seçeneğine göre listele

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    Öğe
    A note on (?, ?)-derivations in prime rings
    (2008) Aydin, Neşet
    Let R be a 2-torsion free prime ring and let ?, ? be automorphisms of R. For any x, y ? R, set [x, y]?, ? = x?(y) - ?(y)x. Suppose that d is a (?, ?)-derivation defined on R. In the present paper it is shown that (i) if d is a nonzero (?, ?)-derivation and h is a nonzero derivation of R such that dh(R) ? C?, ? then R is commutative, (ii) if R satisfies [d(x), x]?, ? ? C?, ?, then either d = 0 or R is commutative. (iii) if I is a nonzero ideal of R such that d(xy) = d(y/x) for all x, y ? I, then R is commutative.
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    Öğe
    Regular elements of the complete semigroups of binary relations of the class ?7(X, 8)
    (2013) Albayrak, Bariş; Diasamidze, I. Yasha; Aydin, Neşet
    In this paper let Q = {T1, T2, T3, T 4, T5, T6, T7, T8} be a subsemilattice of X-semilattice of unions D where T1 ? T 2 ? T3 ? T5 ? T6 ? T8, T1 ? T2 ? T3 ? T5 ? T7 ? T8, T1 ? T2 ? T4 ? T5 ? T6 ? T8, T1 ? T2 ? T4 ? T5 ? T7 ? T8, T1 ? ?, T4\T3 ? ?, T3\T4 ? ?, T6\T7 ? ?, T7\T 6 ? ?, T3 ? T4 = T5, T6 ? T7 = T8, then we characterize the class each element of which is isomorphic to Q by means of the characteristic family of sets, the characteristic mapping and the generate set of Q. Moreover, we calculate the number of regular elements of BX(D) for a finite set X. © 2013 Academic Publications, Ltd.
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    Öğe
    Reverse and jordan (?, ?)? biderivation on prime and semi-prime rings
    (Adiyaman University, 2019) Albayrak, Barış; Aydin, Neşet
    In this study, we prove that any nonzero reverse (?, ?)? biderivation on a prime ring is (?, ?)? biderivation. Also, we show that any Jordan (?, ?)? biderivation on non-commutative semi-prime ring R with char(R)?2 is an (?, ?)? biderivation. In addition, we investigate commutative feature of prime ring with Jordan left (?, ?)? biderivation. © 2019, Adiyaman University. All rights reserved.
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    Öğe
    Some regular elements, idempotents and right units of complete semigroups of binary relations defined by semilattices of the class lower incomplete nets
    (Academic Press, 2014) Diasamidze, Yasha; Erdoğan, Ali; Aydin, Neşet
    In this paper, we investigate such a regular elements ? and idem-potents of the complete semigroup of binary relations BX(D) defined by semi-lattices of the class lower incomplete nets, for which V(D, ?) = Q. Also we investigate right units of the semigroup BX(Q). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of regular elements, idempotents and right units of the respective semigroup. © 2014 Academic Publications, Ltd.
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    Öğe
    Some results for generalized lie ideals in prime rings with derivation II
    (2001) Kaya, Kâzim; Gölbaşi, Öznur; Aydin, Neşet
    Let R be a prime ring of characteristic different from two, d : R ? R a non-zero derivation, and M a non-zero left ideal of R. We prove the following results: (1) if a ? R and [d(R), a]?, ? = 0, then ? (a) + ?(a) ? Z, the center of R, (2) if d([R, a]?, ?) = 0, then ? (a)+?(a) ? Z, (3) if ([R,M]?, ?, a)?, ? = 0, then a ? Z, (4) d(R), a) = 0 if, and only if, d((R, a)) = 0.
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    Öğe
    Some results on semigroup ideals in prime ring with derivations
    (Academic Press, 2016) Ayran, Ayşe; Aydin, Neşet
    Let R be a prime ring, I be a nonzero semigroup ideal of R, d, g, h be derivations of R and a, b ? R. It is proved that if d(x) = ag(x)+h(x)b for all x ? I and a, b are not in Z(R) then there exists for some ? ? C such that h(x) = ? [a, x], g(x) = ? [b, x] and d(x) = ? [ab, x] for all x ? I. © 2016 Academic Publications, Ltd.