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Gupta, Vishnu
- On some Regularity in Semirings
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Authors
Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
2 Department of Mathematics, M. J. College, Jalgaon-425002, IN
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
2 Department of Mathematics, M. J. College, Jalgaon-425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 76, No 1-4 (2009), Pagination: 61-68Abstract
We prove the following theorem: Let R be a right k-semiring whose every simple singular right R-semimodule is p-injective. Then (1) Every large right ideal of R is idempotent. (2) If R has no nonzero nilpotent right ideals, then R is fully right idempotent. (3) If R is right duo, then R is right π-regular.Keywords
Right Regular Semiring, Fully Right Idempotent Semiring, Right π-Regular Semiring, Singular Semimodule, p-Injective Semimodule.- Commutativity of Rings Satisfying a Polynomial Identity
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Theorem. If a ring with identity element 1 satisfies xk[nn,y] = [x,ym]y', for all x,y∈R where n>1 and m are fixed relatively prime positive integers and k,1 are any non-negative integers then R is commutative.
Authors
Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 255-256Abstract
We prove the followingTheorem. If a ring with identity element 1 satisfies xk[nn,y] = [x,ym]y', for all x,y∈R where n>1 and m are fixed relatively prime positive integers and k,1 are any non-negative integers then R is commutative.