IJPAM: Volume 116, No. 3 (2017)

Title

ON PRIME AND SEMIPRIME BI-IDEALS IN
A PARTIALLY ORDERED $\Gamma$-SEMIGROUP

Authors

Thawhat Changphas
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
Centre of Excellence in Mathematics, CHE
Si Ayuttaya Rd., Bangkok, 10400, THAILAND

Abstract

For this paper, we define the concepts of prime and semiprime bi-ideals in a partially ordered $\Gamma$-semigroup. And several properties of them are presented. Indeed, we give a characterization when a bi-ideal of a partially ordered $\Gamma$-semigroup is prime, and prove that a partially ordered $\Gamma$-semigroup is regular if and only if every bi-ideals of the partially ordered $\Gamma$-semigroup is semiprime.

History

Received: 2017-06-21
Revised: 2017-09-27
Published: October 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 20M20, 06F05
Key Words and Phrases: partially ordered $\Gamma$-semigroup (po-$\Gamma$-semigroup), left (right, two-sided) ideal, quasi-ideal, bi-ideal, prime (semiprime) bi-ideal, regular partially ordered $\Gamma$-semigroup

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v116i3.18 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 717 - 725


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