Year 2019, Volume 7, Issue 1, Pages 107 - 111 2019-04-15

A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups

Abul Basar [1]

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In this paper, we investigate the notion of $(m, n)$-ideals in a non-associative algebraic structure, which we call an ordered $LA$-$\Gamma$-semigroup. We prove that if $(S, \Gamma, \cdot, \leq)$ is a unitary ordered $LA$-$\Gamma$-semigroup with zero and $S$ has the condition that it contains no non-zero nilpotent $(m, n)$-ideals and if $R(L)$ is a 0-minimal right (left) ideal of $S$, then either $(R\Gamma L]=\{0\}$ or $(R\Gamma L]$ is a 0-minimal $(m, n)$-ideal of $S$. Also, we prove that if $(S, \Gamma, \cdot, \leq)$ is a unitary ordered $LA$-$\Gamma$-semigroup; $A$ is an $(m, n)$-ideal of $S$ and $B$ is an $(m, n)$-ideal of $A$ such that $B$ is idempotent, then $B$ is an $(m, n)$-ideal of $S$.



$LA$-semigroups
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Author: Abul Basar (Primary Author)
Country: India


Dates

Publication Date: April 15, 2019

Bibtex @research article { konuralpjournalmath483048, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2019}, volume = {7}, pages = {107 - 111}, doi = {}, title = {A Note on \$(m, n)\$-\$\\Gamma\$-Ideals of Ordered \$LA\$-\$\\Gamma\$-Semigroups}, key = {cite}, author = {Basar, Abul} }
APA Basar, A . (2019). A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp Journal of Mathematics (KJM), 7 (1), 107-111. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31492/483048
MLA Basar, A . "A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups". Konuralp Journal of Mathematics (KJM) 7 (2019): 107-111 <http://dergipark.org.tr/konuralpjournalmath/issue/31492/483048>
Chicago Basar, A . "A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups". Konuralp Journal of Mathematics (KJM) 7 (2019): 107-111
RIS TY - JOUR T1 - A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups AU - Abul Basar Y1 - 2019 PY - 2019 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 107 EP - 111 VL - 7 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2019 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups %A Abul Basar %T A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups %D 2019 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 7 %N 1 %R %U
ISNAD Basar, Abul . "A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups". Konuralp Journal of Mathematics (KJM) 7 / 1 (April 2019): 107-111.
AMA Basar A . A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp J. Math.. 2019; 7(1): 107-111.
Vancouver Basar A . A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp Journal of Mathematics (KJM). 2019; 7(1): 111-107.