On the Construction of Polynomial β-algebras over a Field

Keum Sook So<br />Young Hee Kim

doi:10.5666/KMJ.2017.57.1.99

Article

Kyungpook Mathematical Journal 2017; 57(1): 99-108

Published online March 23, 2017

On the Construction of Polynomial β-algebras over a Field

Keum Sook So¹
Young Hee Kim²

Department of Mathematics, Hallym University, Chuncheon 24252, Korea¹
Department of Mathematics, Chungbuk National University, Chongju 28644, Korea²

Received: September 22, 2016; Accepted: November 10, 2016

Abstract

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Abstract

In this paper we construct quadratic β-algebras on a field, and we discuss both linear-quadratic β-algebras and quadratic-linear β-algebras in a field. Moreover, we discuss some relations of binary operations in β-algebras.

Keywords: (linear, quadratic-linear, linear-quadratic) $eta$-algebra, (left, right)-zero semigroup, $BCK$-algebra