The Journal of the Indian Mathematical Society

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On some Regularity in Semirings


Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, India
2 Department of Mathematics, M. J. College, Jalgaon-425002, India
     

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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.
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  • On some Regularity in Semirings

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Authors

Vishnu Gupta
Department of Mathematics, University of Delhi, Delhi-110007, India
J. N. Chaudhari
Department of Mathematics, M. J. College, Jalgaon-425002, India

Abstract


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.