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Abstract
Let S be a semigroup generated by periodic elements and k be an infinite field. Suppose that the
semigroup algebra kS has 1. The authors prove interesting properties of kS and S assuming that
U(kS) satisfies a group identity (kS is called a GIring for short). In particular, S is locally finite
and kS satisfies a polynomial identity. Thus Hartley's conjecture is confirmed for such semigroup
algebras. If, furthermore, S is generated by a finite number of periodic elements, then they give
necessary and sufficient conditions on S for kS to be a GIring. The authors obtain this result by
proving first that if A is a semiprime GIalgebra over an infinite commutative domain D, such that
A is generated as a Dalgebra by U(A) and no element of D is a zero divisor in A, then A is a
reduced ring. The latter fact is also used to give shorter proofs of some known results on group
rings which are GIrings.
semigroup algebra kS has 1. The authors prove interesting properties of kS and S assuming that
U(kS) satisfies a group identity (kS is called a GIring for short). In particular, S is locally finite
and kS satisfies a polynomial identity. Thus Hartley's conjecture is confirmed for such semigroup
algebras. If, furthermore, S is generated by a finite number of periodic elements, then they give
necessary and sufficient conditions on S for kS to be a GIring. The authors obtain this result by
proving first that if A is a semiprime GIalgebra over an infinite commutative domain D, such that
A is generated as a Dalgebra by U(A) and no element of D is a zero divisor in A, then A is a
reduced ring. The latter fact is also used to give shorter proofs of some known results on group
rings which are GIrings.
Original language  English 

Pages (fromto)  273283 
Number of pages  11 
Journal  Journal of Algebra 
Volume  284 
Publication status  Published  2005 
Bibliographical note
Journal of Algebra 284 no. 1 (2005), 273283.Fingerprint
Dive into the research topics of 'On Group Identities for the Unit Group of Algebras and Semigroup Algebras over an Infinite Field'. Together they form a unique fingerprint.Activities
 1 Talk or presentation at a conference

Groups, Rings and Group Rings
Ann Dooms (Speaker)
26 Jul 2004 → 31 Jul 2004Activity: Talk or presentation › Talk or presentation at a conference