Given a family C of closed bounded convex sets in Banach space X, we say that X has the C-MIP if every C∈C is intersection balls containing it. In this paper, introduce stronger version and show it more satisfactory generalisation MIP inasmuch as one can obtain complete analogues various characterisations MIP. We also uniform versions (strong) characterise them analogously. Even case, strong C-...

In this study, the modules whose p-submodules have a complement which is direct summand are explored. The module theoretical properties such as sums and summands investigated. As opposed to sums, condition does not transfer summands. Thus, it examined that under what conditions fulfill property. Examples given demonstrate results.

We consider the ideal structure of a reduced crossed product unital C∗-algebra equipped with an action discrete group. More specifically we find sufficient and necessary conditions for group to have intersection property, meaning that non-zero ideals in restrict underlying C∗-algebra. show property on is equivalent equivariant injective envelope. also centre envelope always contains C∗-algebrai...

We show that a Banach space $X$ has the Uniform Mazur Intersection Property (UMIP) if and only every $f \in S(X^*)$ is uniformly w$^*$-semidenting point of $B(X^*)$. also prove an analogous result for uniform version w$^*$-MIP.

In the present paper, we give a short proof of the nuclearity property of a class of CuntzPimsner algebras associated with a HilbertA-bimodule M, whereA is a separable and nuclear C*-algebra. We assume that the left A-action on the bimodule M is given in terms of compact module operators and that M is direct summand of the standard Hilbert module over A.

We give three proofs that valuation rings are derived splinters: a geometric proof using absolute integral closure, homological which reduces the problem to checking splinters (which is done in second author’s PhD thesis and we reprise here), by approximation Bhatt’s of direct summand conjecture. The property also shows smooth algebras over splinters.

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?