Primitive Near-rings — Some Structure Theorems
Keyword(s):
We show that any zero symmetric 1-primitive near-ring with descending chain condition on left ideals can be described as a centralizer near-ring in which the multiplication is not the function composition but sandwich multiplication. This result follows from a more general structure theorem on 1-primitive near-rings with multiplicative right identity, not necessarily having a chain condition on left ideals. We then use our results to investigate more closely the multiplicative semigroup of a 1-primitive near-ring. In particular, we show that the set of regular elements forms a right ideal of the multiplicative semigroup of the near-ring.
1969 ◽
Vol 10
(1-2)
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pp. 1-4
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1977 ◽
Vol 80
(3)
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pp. 225-229
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1977 ◽
Vol 77
(1-2)
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pp. 145-150
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2012 ◽
Vol 49
(3)
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pp. 366-389
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2009 ◽
Vol 30
(6)
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pp. 1803-1816
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1971 ◽
Vol 14
(3)
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pp. 443-444
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