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FRACTIONAL SKEW MONOID RINGS P. ARA, M.A. GONZ
 

Summary: FRACTIONAL SKEW MONOID RINGS
P. ARA, M.A. GONZ ’
ALEZ­BARROSO, K.R. GOODEARL, AND E. PARDO
Dedicated to the memory of Dmitry Tyukavkin
Abstract. Given an action # 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 S op
## A ## T 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 -1 S, we obtain a G­graded
ring S op
## A ## S with the property that, for each s # S, the s­component 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 # of A. If # is an isomorphism onto a proper corner pAp, we obtain an
analogue of the usual skew Laurent polynomial ring, denoted by A[t + , t - ; #]. 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 - ; #]. Finally, mild
and reasonably natural conditions are obtained under which S op
## A## S is a purely infinite
simple ring.

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics