@misc{10498/16074,
year = {2004},
month = {1},
url = {http://hdl.handle.net/10498/16074},
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  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},
publisher = {Elsevier},
keywords = {Skew monoid ring},
keywords = {Purely infinite simple ring},
keywords = {Leavitt algebra},
title = {Fractional skew monoid rings},
doi = {10.1016/j.jalgebra.2004.03.009},
author = {Ara, P. and González-Barroso, M.A. and Goodearl, K.R. and Pardo Espino, Enrique},
}