IJPAM: Volume 101, No. 3 (2015)

MODULAR, PRIMITIVE PROPERTIES AND CHAIN
CONDITIONS IN RIGHT TERNARY NEAR-RINGS

A. Uma Maheswari$^1$, C. Meera$^2$
$^1$Department of Mathematics
Quaid-E-Millath Government College for Women (Autonomous)
Chennai, 600 002, Tamil Nadu, INDIA
$^2$Department of Mathematics
Bharathi Women's College (Autonomous)
Chennai, 600 108, Tamil Nadu, INDIA


Abstract. A study on Right Ternary Near-Ring (RTNR) paves a way for a deeper understanding of its binary counterpart. In this paper the necessary and sufficient for an RTNR $N$ to have chain conditions is given. The existence of a right unital element in a monogenic $N$-subgroup of a zero-symmetric RTNR $N$ with Descending Chain Condition (DCC) on left $N$-subgroups is established. Modular ideals are introduced in this generalised setting and it is proved that the intersection of two modular ideals $L_1$ and $L_2$ is a modular ideal if the zero-symmetric distributive RTNR $N$ is the sum of $L_1$ and $L_2$. If $N$ is a right and lateral ternary near-ring then for $\nu \in \{0, 1,
2\}$, $\nu$-modular left ideals and $\nu$-primitivity are defined. The interrelationship between the different types of $\nu$-primitive ideals is also discussed.

Received: July 29, 2014

AMS Subject Classification: 20N10, 16Y30, 16P70, 16D25, 16D60

Key Words and Phrases: RTNR, ideals, monogenic $N$-groups, quotient RTNR, unital element

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DOI: 10.12732/ijpam.v101i3.3 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: 2015
Volume: 101
Issue: 3
Pages: 349 - 368


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