JP Journal of Algebra, Number Theory and Applications
Volume 1, Issue 2, Pages 115 - 124
(August 2001)
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A
GENERALIZATION OF STRONG REGULARITY IN NEAR-RINGS
Yong Uk Cho (Korea)
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Abstract: In
this paper, we investigate some
characterizations of left strongly regularity
in near-rings viz. the four equivalent
concepts of left strong regularity under the
zero symmetric near-ring and from this we
obtain 9-equivalent conditions for strong
regularity of an arbitrary ring.
Next, we introduce a general concept of strong
regularity in near-rings known as the strongly
reduced near-ring and investigate several
properties of near-rings under strong
reducibility. For an example, every idempotent
is right semicentral, ab = 0 implies ba
= b0, and also the notions of p-regularity
and left strong p-regularity
are equivalent in near-rings. |
Keywords and phrases: structured
matrices, tridiagonal, Toeplitz. |
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