Korean J. Math.  Vol 26, No 1 (2018)  pp.143-153
DOI: http://dx.doi.org/10.11568/kjm.2018.26.1.143

On $0$-minimal $(m, n)$-ideal in an LA-semigroup

Thiti Gaketem

Abstract


In this paper, we define $0$-minimal $(m, n)$-ideals in an LA-semigroup $S$ and prove that if $R (L)$ is a 0-minimal right (left) ideal of $S$,  then either $R^mL^n = \{0\}$ or $R^mL^n$ is a $0$-minimal $(m, n)$-ideal of $S$ for $m, n \geq 3$.


Keywords


LA-semigroup, ideal, $0$-minimal $(m, n)$-ideal , $(m, n)$-regular.

Subject classification

20M10, 20N99

Sponsor(s)

School of Science, University of Phayao grant.

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