On an additive ideal theory in a non-associative ring.

Yoshiki Kurata

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Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X^⊥ of a subset X of R is zero, then X₁ ^⊥ = 0 for a finite subset X₁ ⊆ X. (ZIP 2) If L is a left ideal and if L^⊥ = 0, then L₁ ...

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Split-null extensions of strongly right bounded rings.

Gary F. Birkenmeier (1990)

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A ring is said to be strongly right bounded if every nonzero right ideal contains a nonzero ideal. In this paper strongly right bounded rings are characterized, conditions are determined which ensure that the split-null (or trivial) extension of a ring is strongly right bounded, and we characterize strongly right bounded right quasi-continuous split-null extensions of a left faithful ideal over a semiprime ring. This last result partially generalizes a result of C. Faith concerning split-null...