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Units in finite loop algebras of $R A 2$ loops

Swati Sidana

Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

E-mail Address: swatisidana@gmail.com

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and

R. K. Sharma

Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

E-mail Address: rksharmaiitd@gmail.com

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https://doi.org/10.1142/S1793557116500261Cited by:1 (Source: Crossref)

Abstract

Let $F [L]$ be the loop algebra of a loop $L$ over a field $F$ . In this paper, we characterize the structure of the unit loop of $F [L]$ modulo its Jacobson radical when $L = M (D_{2 m}, 2)$ is an $R A 2$ loop obtained from the dihedral group of order $2 m$ , $m$ is an odd number and $F$ is a finite field of characteristic $2$ . The structure of $1 + J (F [L])$ is also determined.

Communicated by N. Gilbert

Keywords:

AMSC: 20N05, 17D05

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