Multiplicative ideal theory of noncommutative Krull pairs. II: Factorization of one-sided ideals

A (one-sided) Prime Ideal Principle for Noncommutative Rings

In this paper we study certain families of right ideals in noncommutative rings, called right Oka families, generalizing previous work on commutative rings by T.Y. Lam and the author. As in the commutative case, we prove that the right Oka families in a ring R correspond bijectively to the classes of cyclic right R-modules that are closed under extensions. We define completely prime right ideal...

On One-Sided Ideals of Rings of Linear Transformations

Multiplicative Ideal Theory

on one-sided ideals of rings of linear transformations

ONE - SIDED k - IDEALS ANDh - IDEALS IN SEMIRINGSH

ideals of these kinds; congruence class semirings. Abstract: Since they are closer related to the ring-theoretical concept of ideals than arbitrary semiring ideals, two-sided k-ideals and h-ideals occur in several statements on semirings. In this paper we investigate those ideals and also left-sided ones in arbitrary semirings S with commutative addition. For instance, we prove (for the rst tim...