IJPAM: Volume 101, No. 3 (2015)
CONDITIONS IN RIGHT TERNARY NEAR-RINGS



Quaid-E-Millath Government College for Women (Autonomous)
Chennai, 600 002, Tamil Nadu, INDIA

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 to have chain conditions is given. The
existence of a right unital element in a monogenic
-subgroup of a
zero-symmetric RTNR
with Descending Chain Condition (DCC) on left
-subgroups is established. Modular ideals are introduced in this
generalised setting and it is proved that the intersection of two
modular ideals
and
is a modular ideal if the
zero-symmetric distributive RTNR
is the sum of
and
. If
is a right and lateral ternary near-ring then for
,
-modular left ideals and
-primitivity are defined. The
interrelationship between the different types of
-primitive
ideals is also discussed.
Received: July 29, 2014
AMS Subject Classification: 20N10, 16Y30, 16P70, 16D25, 16D60
Key Words and Phrases: RTNR, ideals, monogenic -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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This work is licensed under the Creative Commons Attribution International License (CC BY).