منابع مشابه
Center--like subsets in rings with derivations or epimorphisms
We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.
متن کاملOn constant products of elements in skew polynomial rings
Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...
متن کاملOn dependent elements in rings
out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...
متن کاملcenter--like subsets in rings with derivations or epimorphisms
we introduce center-like subsets z*(r,f), z**(r,f) and z1(r,f), where r is a ring and f is a map from r to r. for f a derivation or a non-identity epimorphism and r a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of r.
متن کاملNilpotent Elements in Skew Polynomial Rings
Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1985
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171285000138