Yazar "Camci, Didem Karalarlioglu" seçeneğine göre listele

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    Öğe
    Some results on prime rings with multiplicative derivations
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Sandhu, Gurninder Singh; Camci, Didem Karalarlioglu
    Let R be a prime ring with center Z(R) and an automorphism a. A mapping delta : R -> R is called multiplicative skew derivation if delta(xy) = delta(x)y + alpha(x)delta(y) for all x, y is an element of R and a mapping F : R -> R is said to be multiplicative (generalized)-skew derivation if there exists a unique multiplicative skew derivation delta such that F(xy) = F(x)y + alpha(x)delta(y) for all x, y is an element of R. In this paper, our intent is to examine the commutativity of R involving multiplicative (generalized)-skew derivations that satisfy the following conditions: (i) F(x(2)) + x delta(x) = delta(x(2)) + xF(x), (ii) F(x circle y) = delta(x circle y) +/- x circle y, (iii) F([x, y]) = delta([x, y])+/-[x, y], (iv) F(x(2)) = delta(x(2)), (v) F([x, y]) = +/- x(k) [x, delta(y)]x(m), (vi) F(x circle y) = +/- x(k)(x circle delta(y))x(m), (vii) F([x, y]) = +/- x(k) [delta(x), y]x(m), (viii) F(x circle y) = +/- x(delta(x) circle y)x(m) for all x, y is an element of R.
  • [ X ]
    Öğe
    THE SOURCE OF SEMIPRIMENESS OF RINGS
    (Korean Mathematical Soc, 2018) Aydin, Neset; Demir, Cagri; Camci, Didem Karalarlioglu
    Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar-domain and a vertical bar S-R vertical bar-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite vertical bar S-R vertical bar-domain is necessarily unitary, and is in fact a vertical bar S-R vertical bar-division ring. However, we provide an example showing that a finite vertical bar S-R vertical bar-division ring does not need to be commutative. All possible values for characteristics of unitary vertical bar S-R vertical bar-reduced rings and vertical bar S-R vertical bar-domains are also determined.