IJPAM: Volume 97, No. 2 (2014)

QUASI-INJECTIVE NEAR-RING GROUPS

Navalakhi Hazarika$^1$, Helen K. Saikia$^2$
$^1$Department of Mathematics
Royal School of Engineering and Technology
Guwahati, 781035, INDIA
$^2$Department of Mathematics
Gauhati University
Guwahati, 781014, INDIA


Abstract. We extend the concepts of quasi-injective modules and their endomorphism rings to near-ring groups. We attempt to derive the near-ring character of the set of endomorphism of quasi-injective $N$-groups under certain conditions and this leads us to a near-ring group structure which motivates us to study various characteristics of the structure. If $E$ is a quasi-injective N-group and $S = End(injective\, hull\, of\, E)$ then we study the structure $ES$ and various properties of $ES$. It is proved that $ES$ is a minimal quasi-injective extension of $E$ and any two minimal quasi-injective extensions are equivalent. This structure motivates to study the Jacobson radical of endomorphism near-ring of quasi-injective $N$-group $E$. It is established that the near-ring modulo the Jacobson radical is a regular near-ring. Some properties of quasi-injective $N$-groups relating essentially closed $N$-subgroups and complement $N$-subgroups are established.

Received: June 19, 2014

AMS Subject Classification: 16Y30

Key Words and Phrases: near-ring groups, quasi-injective $N$-subgroups, essentially closed $N$-subgroups

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DOI: 10.12732/ijpam.v97i2.8 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: 2014
Volume: 97
Issue: 2
Pages: 201 - 210


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