Korean J. Math. Vol. 34 No. 2 (2026) pp.243-247
DOI: https://doi.org/10.11568/kjm.2026.34.2.243

On linear groupoids and quadratic algebras over reals

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Published: Jun 30, 2026
Keywords:
groupoid, linear groupid, quadratic algebra, associative law
Mathematics Subject Classification:
20N02

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Young Hie Kim
Bangmok College of General Education, Myongji University, Yongin 17058, Korea
Hee Sik Kim
Department of Mathematics, Hanyang University, Seoul 04763, Korea
Sun Shin Ahn
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea

Abstract

In this paper, we characterize quadratic algebras over reals having identity, and show that there is no proper quadratic algebra with identity satisfying the inverse axiom over reals.



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