IJPAM: Volume 114, No. 3 (2017)

Title

RIGHTIDEALS IN $\Gamma$-SEMIGROUPS

Authors

V. Jyothi, Y. Sarala$^2$, Rao T. Nageshwara$^3$, Rao D. Madhusudhana$^4$
$^1$Department of Mathematics
K.L. University
Guntur Dt., A.P., INDIA
$^2$Department of Mathematics
NIT A.P., K.L. University
Guntur Dt., A.P., INDIA

Abstract

In This article to prove an equivalent of the krull- intersection theorem $ \cap _{m = 1} ^{\infty} M^{m} = 0 $ in 2.11 and thus it is shown that the $\Gamma$ - semigroup with the krull - intersection property is nearly a principal $\Gamma$ - rightideal $\Gamma$ - semigroup. Every principal $\Gamma$ - rightideal $\Gamma$ - semigroup need not have the krull - intersection property and so it is researched what type of principal $\Gamma$ - rightideal $\Gamma$ - semigroups, not vitally containing an identity, have this intersection property. It is initiate in 2.11, 2.13 and 3.1, that the equivalent of the krull - intersection theorem is true under some additional conditions unlike in ring theory.

History

Received: December 17, 2016
Revised: May 20, 2017
Published: May 23, 2017

AMS Classification, Key Words

AMS Subject Classification: 20M10, 20M99
Key Words and Phrases: principal $\Gamma$- rightideal, $\Gamma$- right Noetherian, $\Gamma$- right uniform

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Bibliography

How to Cite?

DOI: 10.12732/ijpam.v114i3.8 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: 114
Issue: 3
Pages: 515 - 521


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