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- W2022993805 abstract "Given an action α of a monoid T on a ring A by ring endomorphisms, and an Ore subset S of T, a general construction of a fractional skew monoid ring Sop∗αA∗αT is given, extending the usual constructions of skew group rings and of skew semigroup rings. In case S is a subsemigroup of a group G such that G=S−1S, we obtain a G-graded ring Sop∗αA∗αS with the property that, for each s∈S, the s-component contains a left invertible element and the s−1-component contains a right invertible element. In the most basic case, where G=Z and S=T=Z+, the construction is fully determined by a single ring endomorphism α of A. If α is an isomorphism onto a proper corner pAp, we obtain an analogue of the usual skew Laurent polynomial ring, denoted by A[t+,t−;α]. Examples of this construction are given, and it is proven that several classes of known algebras, including the Leavitt algebras of type (1,n), can be presented in the form A[t+,t−;α]. Finally, mild and reasonably natural conditions are obtained under which Sop∗αA∗αS is a purely infinite simple ring." @default.
- W2022993805 created "2016-06-24" @default.
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- W2022993805 date "2004-08-01" @default.
- W2022993805 modified "2023-09-26" @default.
- W2022993805 title "Fractional skew monoid rings" @default.
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- W2022993805 doi "https://doi.org/10.1016/j.jalgebra.2004.03.009" @default.
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