منابع مشابه
Derivations in semiprime rings and Banach algebras
Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...
متن کاملRees cones and monomial rings of matroids
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some application...
متن کاملF-Rationality of Determinantal Rings and Their Rees Rings
Let X be an m × n matrix (m ≤ n) of indeterminates over a field K of positive characteristic, and denote the ideal generated by its t-minors by It . We show that the Rees ringR(It ) ofK[X], as well as the algebra At generated by the t-minors, are F-rational if charK > min(t, m − t). Without a restriction on characteristic this holds for K[X]/Ir+1 and the symbolic Rees ring R(It ). The determina...
متن کاملGeneralized Derivations of Prime Rings
Let R be an associative prime ring, U a Lie ideal such that u2 ∈ U for all u ∈ U . An additive function F : R→ R is called a generalized derivation if there exists a derivation d : R→ R such that F(xy)= F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any one of the following conditions holds: (1) d(x) ◦F(y)= 0, (2) [d(x),F(y) = 0], (3) either d(x) ◦ F(y) ...
متن کاملSome Constructions Related to Rees Matrix Rings
Simple rings with a one-sided minimal ideal may be represented as Rees matrix rings, and conversely. The latter are defined as I ×Λ matrices over a division ring with only a finite number of nonzero entries with certain addition and multiplication. For Rees matrix rings we construct here their isomorphisms, their translational hulls and isomorphisms of the translational hulls, all this in terms...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1994
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181072354