Research Journal of Science and Technology

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Going Up and Going Down Relations for Partial Actions on Algebras


Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-5, India
     

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In this article, we consider a K − algebra R with a partial action α of a finite group G on it. If each g Dg is generated by a central idempotent of R, we answer the question: If P1 ⊂ P2 are primes in R and P2 minimal over P2∩ Rα, does some prime P1 exist in Rα such that P1 is minimal over P2∩ Rα, and P1⊂p2? Similar results are proved by interchanging R and Rα.
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  • Going Up and Going Down Relations for Partial Actions on Algebras

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Authors

R. P. Sharma
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-5, India
Anu
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-5, India

Abstract


In this article, we consider a K − algebra R with a partial action α of a finite group G on it. If each g Dg is generated by a central idempotent of R, we answer the question: If P1 ⊂ P2 are primes in R and P2 minimal over P2∩ Rα, does some prime P1 exist in Rα such that P1 is minimal over P2∩ Rα, and P1⊂p2? Similar results are proved by interchanging R and Rα.

References