The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 89-165
Full Name: Jalal Karam
Position: Associate Professor
Age: ON
Sex: Male
Address: Alfaisal University, Al Maathar Road, Box 50927, Riyadh 11533
Country: SAUDI ARABIA
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E-mail address: jkaram@alfaisal.edu
Other E-mails: karamjr@canada.com
Title of the Paper: Extended Results On Commutative and Nil - Semiclean Rings
Authors as they appear in the Paper: Jalal Karam, Omar Mallah
Email addresses of all the authors: jkaram@alfaisal.edu, Omarmallah@yahoo.com
Number of paper pages: 10
Abstract: – If a ring R is a nil-semiclean ring then the Jacobson radical of R J(R) is also nil and that if R is a nil-clean ring and the idempotents of R are centrals, then the Jacobson radical of R equals to the set of all nilpotents of R. These results were obtained in previous work by the authors. In this paper, we include work out examples and extend results on orthogonal idempotents elements in R. If e is central idempotent in R, then conditions for R to be nil-clean and nil-semiclean are justified. For a central idempotent element e of a ring R we show that If eRe and fRf are nil-clean rings then R is a nil-clean ring and if eRe and fRf are nil-semiclean rings then R is nil-semiclean ring. Finally, we proved that if R is a commutative ring then the polynomial ring R[x] is not nil-semiclean.
Keywords: Commutative Ring, Orthogonal Idempotent, Clean and Semiclean, Nil-Semiclean, Jacobson Radical.
EXTENSION of the file: .doc
Special (Invited) Session: On Commutative and Nil - Semiclean Rings
Organizer of the Session: 629-139
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