Fractional skew monoid rings

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URI: http://hdl.handle.net/10498/16074
DOI: 10.1016/j.jalgebra.2004.03.009
ISSN: 0021-8693
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2004-01-01Department
MatemáticasSource
Journal of Algebra 278 (2004), 104-126Abstract
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 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 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 and , 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 is a purely infinite simple ring
Subjects
Skew monoid ring; Purely infinite simple ring; Leavitt algebraCollections
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