Near-rings with no non-zero nilpotent two-sidedR-subsets |
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Authors: | A. K. Goyal S. C. Choudhary |
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Affiliation: | (1) 40 Ravindra Nagar, 313001 Udaipur, RAJ., India |
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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-ringsRi (1 i n) where eachRi is simple and strictly prime. |
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Keywords: | Primary 16A76 Secondary 16A34 |
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