Research Journal of Science and Technology

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Going Up and Going Down Relations for Partial Actions on Algebras


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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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  • Dokuchaev, M., Exel, R. (2005). Associativity of crossed products by partial actions, enveloping actions and partial representations. Trans. Amer. Math. Society 357(5):1931-1952.

  • Dokuchaev, M., Ferrero, M., Paques, A. (2007). Partial actions and Galois Theory. J. Pure Apll. Algebra 208:77-87.

  • Montgomery, S. (1989). Prime ideals and Group actions in Noncommutative Algebras. Contemporary Mathematics 89:103-124.

  • Sharma, R. P., Anu (Submitted in "Comm. in Algebra"). Prime ideals and partial group actions on Algebras.


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  • Going Up and Going Down Relations for Partial Actions on Algebras

Abstract Views: 695  |  PDF Views: 0

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