1,229 research outputs found
A decomposition theorem for semiprime rings
A ring A is called an F DI-ring if there exists
a decomposition of the identity of A in a sum of finite number
of pairwise orthogonal primitive idempotents. We call a primitive idempotent e artinian if the ring eAe is Artinian. We prove
that every semiprime F DI-ring is a direct product of a semisimple
Artinian ring and a semiprime F DI-ring whose identity decomposition doesn’t contain artinian idempotents
PI theory for Associative Pairs
We extend the classical associative PI-theory to Associative Pairs, and in
doing so, we introduce related notions already present for algebras (and Jordan
systems) as the ones of PI-element and PI-ideal, extended centroid and central
closure
Prime Structures in a Morita Context
In this paper, we study on the primeness and semiprimeness of a Morita
context related to the rings and modules. Necessary and sufficient conditions
are investigated for an ideal of a Morita context to be a prime ideal and a
semiprime ideal. In particular, we determine the conditions under which a
Morita context is prime and semiprime
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.Comment: 8 page
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