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 A-module with basis L, with a multiplication induced distributively from the operation in L.
The author was partially supported by a research grant from CNPq., Proc. 300243/79–0(RN)
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Milies, C.P. (1999). Alternative Loop Rings and Related Topics. In: Passi, I.B.S. (eds) Algebra. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9996-3_9
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