Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. For α = α in a loop ring RL, define α = α −1 and call α symmetric if α = α. We find necessary and sufficient conditions under which the symmetric units are closed under multiplication (and hence form a subloop of the loop of units in RL) when R has characteristic two and when R = Z, the ring of rational integers. CNPq., Proc. 300243/79-0(RN) of Brasil. Algebra Colloq. 2006.13:361-370. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 02/05/15. For personal use only. Algebra Colloq. 2006.13:361-370. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 02/05/15. For personal use only.
Let G be a finite abelian group and F a field such that char(F) | |G|. Denote by FG the group algebra of G over F. A (semisimple) abelian code is an ideal of FG. Two codes I1 and I2 of FG are G-equivalent if there exists an automorphism ψ of G whose linear extension to FG maps I1 onto I2.In this paper we give a necessary and sufficient condition for minimal abelian codes to be G-equivalent and show how to correct some results in the literature.Index Terms-group algebra, G-equivalence, primitive idempotent, abelian codes.
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