One Sided Ideals and Carlson’s Theorem

On One-Sided Ideals of Rings of Linear Transformations

On Ideals Which Have the Weakly Insertion of Factors Property

A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...

Sharpening and Generalizations of Carlson’s Inequality for the Arc Cosine Function

In this paper, we sharpen and generalize Carlson’s double inequality for the arc cosine function.

A Note on Chain Conditions in Nilpotent Rings and Groups

Maximal and minimal conditions for ideals in associative rings have often been considered, but little seems to be known of these conditions in non-associative rings, or of chain conditions on the non-normal subgroups of a group. Moreover, it is usual to assume the condition for one-sided ideals in noncommutative rings, and the weaker condition for two-sided ideals rarely appears. In this note w...

A Characterization and Sum Decomposition for Operator Ideals

Let L(H) be the ring of bounded operators on a separable Hubert space. Assuming the continuum hypothesis, we prove that in L(H) every two-sided ideal that contains an operator of infinite rank is the sum of two smaller two-sided ideals. The proof involves a new combinatorial description of ideals of L(H). This description is also used to deduce some related results about decompositions of ideal...