arXiv subjects

Shervin Sahebi

Publications and source records attributed to Shervin Sahebi.

8 recordsLinked to original sources

arXiv2014

On a generalization of McCoy Rings

We introduce Central McCoy rings, which are a generalization of McCoy rings and investigate their properties. For a ring R, we prove that R is right Central McCoy if and only if the polynomial ring R[x] is right Central McCoy. Also, we give some examples to show that if R is right Central McCoy, then Mn(R) and Tn(R) are not necessary right Central McCoy, but Dn(R) and Vn(R) are right Central McCoy, where Dn(R) and Vn(R) are the subrings of the triangular matrices with constant main diagonal and constant main diagonals, respectively.

math.RA↗

arXiv2014

On a generalization of NC-McCoy Rings

In the present paper we concentrate on a natural generalization of NC-McCoy rings that is called J-McCoy and investigate their properties. We prove that local rings are J-McCoy. Also, for an abelian ring R, we show that R is J-McCoy if and only if eR is J-McCoy, where e is an idempotent element of R. Moreover, we give an example to show that the J-McCoy property does not pass Mn(R), but S(R; n);A(R; n);B(R; n) and T(R; n) are J-McCoy

math.RA↗

arXiv2014

On A Generalization of Weak Armendariz Rings

We introduce the notion of J-Armendariz rings, which are a generalization of weak Armendariz rings and investigate their properties. We show that any local ring is J-Armendariz, and then fined a local ring that is not weak Armendariz.

math.RA↗

arXiv2014

On Central Skew Armendariz rings

For a ring endomirphism, we introduce the central skew Armendariz rings, which are a generalization of skew Armendariz rings and central Armendariz rings, and investigate their properties.

math.RA↗

arXiv2014

A note on power values of derivation in prime and semiprime rings

Let R be a ring with derivation d, such that (d(xy))^n =(d(x))^n(d(y))^n for all x,y in R and n>1 is a fixed integer. In this paper, we show that if R is a prime, then d = 0 or R is a commutative. If R is a semiprime, then d maps R in to its center. Moreover, in semiprime case let A = O(R) be the orthogonal completion of R and B = B(C) be the Boolian ring of C, where C is the extended centroid of R, then there exists an idempotent e in B such that eA is commutative ring and d induce a zero derivation on (1-e)A.

math.RA↗

arXiv2014

Generalized derivations as a generalization of Jordan homomorphisms acting on Lie ideals and right ideals

Let R be a prime ring with center Z(R) and extended centroid C, H a non-zero generalized derivation of R and n>1 a fixed integer. In this paper we study the situations: (1) H(u2)n-H(u)2n in C for all u in L, where L is a non-central Lie ideal of R; (2) H(u2)n - H(u)2n = 0 for all u in [I; I], where I is a nonzero right ideal of R.

math.RA↗

arXiv2014

Rings in which power values of K-Engels with derivations annihilate a certain element

Let R be a 2 torsion free semiprime ring and d a nonzero derivation. Further let A = O(R) be the orthogonal completion of R and B = B(C) the Boolean ring of C where C be the extended centroid of R. We show that if a[[d(x),x]^n- [y, d(y)]^m]^t = 0 such that a in R for all x, y in R, where m, n, t > 0 are fixed integers, then there exists an idempotent e in B such that eA is a commutative ring and d induce a zero derivation on (1-e)A.

math.RA↗

arXiv2014

Generalized derivations with central values on lie ideals LIE IDEALS

Let R be a prime ring of H a generalized derivation and L a noncentral lie ideal of R. We show that if l^sH(l)l^t in Z(R) for all lin2 L, where s, t> 0 are fixed integers, then H(x) = bx for some b in C, the extended centroid of R, or R satisfies S4. Moreover, let R be a 2-torsion free semiprime ring, let A = O(R) be an orthogonal completion of R and B = B(C) the Boolean ring of C. Suppose ([x1; x2]sH([x1; x2])[x1; x2]t in Z(R) for all x1; x2 in R, where s, t> 0 are fixed integers. Then there exists idempotent e in B such that H(x) = bx on eA and the ring (1-e)A satisfies S4.

math.RA↗