The modern theory of linear codes over a finite ring relies heavily on the algebraic structure of the ring of complex-valued functions on a finite ring R. So motivated, this paper applies the theory of semigroup rings to the more general case of K[R], the ring of K-valued functions of finite support over an arbitrary ring R for a field K of characteristic zero. We provide several structural results for K[R], such as a characterization of the semiprimeness of K[R] for commutative R and sufficient conditions for the subring of invariant functions of K[R] to be semisimple and Artinian.

semigroup rings, semiprime, function rings, invariant functions.

Received: December 26, 2020; Accepted: January 16, 2021; Published: February 22, 2021

How to cite this article: Yasuyuki Hirano, Brent Solie and Hisaya Tsutsui, The semiprimeness of semigroup rings, JP Journal of Algebra, Number Theory and Applications 49(2) (2021), 121-138. DOI: 10.17654/NT049010121

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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