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Rings virtually satisfying a polynomial identity
- Source :
-
Journal of Pure & Applied Algebra . Jun2005, Vol. 198 Issue 1-3, p9-19. 11p. - Publication Year :
- 2005
-
Abstract
- Abstract: Let R be a ring and be a polynomial in noncommutative indeterminates with coefficients from and zero constant. The ring R is said to be an f-ring if for all of R and a virtually f-ring if for every n infinite subsets (not necessarily distinct) of R, there exist n elements such that . Let be the ‘smallest’ ring (in some sense) with identity containing R such that . Then denote by the subring generated by the identity of and denote by the image of f in (the ring of polynomials with coefficients in in commutative indeterminates ). In this paper, we show that if R is a left primitive virtually f-ring such that , then R is finite. Using this result, we prove that an infinite semisimple virtually f-ring R is an f-ring, if the subring of generated by the coefficients of is equal to ; and we also prove that if , where , then every infinite virtually f-ring with identity is a commutative f-ring. Finally we show that a commutative Noetherian virtually f-ring R with identity is finite if the subring generated by the coefficients of is . [Copyright &y& Elsevier]
- Subjects :
- *POLYNOMIALS
*APPROXIMATION theory
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 198
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 17664699
- Full Text :
- https://doi.org/10.1016/j.jpaa.2004.11.008