A module M is said to have the SIP if intersection of each pair direct summands also a summand M. In this article, we define SIPr and only exact where r left preradical for category right modules. We investigate structural properties SIPr-modules locate implications between other properties. deal with decomposition theory as well SIPr-modules. provide examples by looking at special preradicals.

Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...

Let K(n)∗(−) be a Morava K-theory at the prime 2. Invariant theory is used to identify K(n)∗(BA4) as a summand of K(n)∗(BZ/2 × BZ/2). Similarities with H∗(BA4;Z/2) are also discussed.

Mahowald proved the height 1 telescope conjecture at prime 2 as an application of his seminal work on bo-resolutions. In this paper we study through lens tmf-resolutions. To end compute structure tmf-resolution for a specifc type complex Z. We find that, analogous to case, E1-page possesses decomposition into v2-periodic summand, and Eilenberg-MacLane summand which consists bounded v2-torsion. ...

@We show that for a twist knot, the A-polynomial can be obtained from recurrences for the summand in Masbaum’s formula of the colored Jones polynomial. Our result supports the AJ conjecture due to S.Garoufalidis.

It is known that in the case of convergence to a normal law, the uniform rate of convergence is completely determined by the rate of convergence at points near the origin, up to terms of order n~; see [6, pp. 12, 46]. In this paper we show that results of this nature hold true for convergence to non-normal stable laws, provided the centering point is taken as the mode of the limit distribution....