Partial Group Representations on Semialgebras
Meenakshi1, R. P. Sharma2
1Dr. Meenakshi, Srinivasa Ramanujan Department of Mathematics Central University of Himachal Pradesh Shahpur, Kangra India.
2Prof. R.P. Sharma, Department of Mathematics and Statistics Himachal Pradesh University Summerhill, Shimla, India.
Manuscript received on 24 February 2023 | Revised Manuscript received on 16 March 2023 | Manuscript Accepted on 15 April 2023 | Manuscript published on 30 April 2023 | PP: 20-25 | Volume-3 Issue-1, April 2023 | Retrieval Number: 100.1/ijam.A1147043123 | DOI: 10.54105/ijam.A1147.043123
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Abstract: Let A bean additively cancellative semialgebra over an additively cancellative semifield K as defined in [9]. For a given partial action α of a group G on an algebra, the associativity of partial skew group ring together with the existence and uniqueness of enveloping (global) action were studied by M. Dokuchaev and R. Exel [2] which were extended for semialgebras with some restriction by Sharma et. al. using the ring of differences. In a similar way, we extend the results of [2,3] for semialgebras regarding partial representations.
Keywords: Semialgebras; partial group actions; partial representations. AMS Subject Classification: 22E46, 53C35, 57S20
Scope of the Article: Algebra