On primeness of general skew inverse Laurent series ring

Abstract

ABSTRACTEver since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x−1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ.