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- Title
EXTENSIONS OF HOMOGENEOUS SEMILOCAL RINGS I.
- Authors
EL-DEKEN, SUSAN F.
- Abstract
A ring R with Jacobson radical J(R) is a homogeneous semilocal ring if R/J(R) is simple artinian. In this paper, we study the transfer of the property of being homogeneous semilocal from a ring R to the formal power series ring R[[x]], the skew formal power series ring R[[x, α]] and the Hurwitz series ring HR. The results of the paper generalize those proved for commutative local rings. We also consider finite centralizing extensions proving that if the ring of matrices Mn(R) is a homogeneous semilocal ring, then so is R. More generally, if e is an idempotent of a homogeneous semilocal ring S, then eSe is homogeneous semilocal.
- Subjects
FIELD extensions (Mathematics); SEMILOCAL rings; RING theory; JACOBSON radical; ARTIN rings; POWER series rings; COMMUTATIVE rings
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 5, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498813501570