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Erschienen in:
1999 | OriginalPaper | Buchkapitel
Alternative Loop Rings and Related Topics
verfasst von : César Polcino Milies
Erschienen in: Algebra
Verlag: Hindustan Book Agency
Enthalten in: Professional Book Archive
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Let R be a commutative (and associative) ring with unity and let L be a loop (roughly speaking, a loop is a group which is not necessarily associative, see Definition 3.1). The loop algebra of L over R was introduced in 1944 by R.H. Bruck (1944) as a means to obtain a family of examples of nonassociative algebras and is defined in a way similar to that of a group algebra; i.e., as the free R-module with basis L, with a multiplication induced distributively from the operation in L.