ISSN:
1588-2829
Keywords:
Primary 16A76
;
Secondary 16A34
;
R-subset
;
subdirect sum
;
S-near ring
;
regular
;
strictly prime ideal
;
strictly prime near-ring
;
simple
;
right duo
;
modular ideal
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract It has been proved that, ifR is a near-ring with no non-zero nilpotent two-sidedR-subsets and if the annihilator of any non-zero ideal is contained in some maximal annihilator, thenR is a subdirect sum of strictly prime near-rings. Moreover, ifR is a near-ring with no non-zero nilpotent two-sidedR-subsets and satisfying a.c.c. or d.c.c. on annihilating ideals of the form Ann (Q), whereQ is an ideal ofR, thenR is a finite subdirect sum of strictly prime near-rings. It is also proved that, ifR is a regular and right duo near-ring that satisfies a.c.c. (or d.c.c.) on annihilating ideals of the form Ann (Q), whereQ is an ideal ofR, thenR is a finite direct sum of near-ringsR i (1 ≤i ≤ n) where eachR i is simple and strictly prime.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01848154
Permalink
