ON STRONG FORM OF REDUCEDNESS

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 1,  2008, pp.1-7
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.1.001
Title & Authors
ON STRONG FORM OF REDUCEDNESS
Cho, Yong-Uk;

Abstract
A near-ring N is said to be strongly reduced if, for a $\small{{\in}}$ N, $\small{a^2{\in}N_c}$ implies $\small{a{\in}N_c}$, where $\small{N_c}$ denotes the constant part of N. We investigate some properties of strongly reduced near-rings and apply those to the study of left strongly regular near-rings. Finally we classify all reduced and strongly reduced near-rings of order $\small{{\leq}}$ 7 using the description given in J. R. Clay [1].
Keywords
left strongly regular near-rings;strongly reduced near-rings;periodic near-rings;
Language
English
Cited by
References
1.
J. R. Clay, The near-rings on groups of low order, Math. Z. 104 (1968), 364-371.

2.
P. Dheena, A generalisation of strongly regular near-rings, Indian J. Pure and Appl. Math. 20 (1989), 58-63.

3.
M. Hongan, Note on strongly regular near-rings, Proc. Edinburgh Math. Soc. 29 (1986), 379-381.

4.
G. Mason, Strongly regular near-rings, Proc. Edinburgh Math. Soc. 23 (1980), 27-35.

5.
G. Mason, A note on strong forms of regularity for near-rings, Indian J. of Math. 40(2) (1998), 149-153.

6.
C. V. L. N. Murty, Generalized near-fields, Proc. Edinburgh Math. Soc. 27 (1984), 21-24.

7.
G. Pilz, Near-Rings, North-Holland Publishing Company, Amsterdam-New York-Oxford, 1983.

8.
D. Ramakotaiah and V. Sambasivarao, Reduced near-ring, in Near-rings and Near-fields, G. Betsch (editor), North-Holland (1987), 233-243.

9.
Y. V. Reddy and C. V. L. N. Murty, On strongly regular near-rings, Proc. Edinburgh Math. Soc. 27 (1984), 61-64.