This paper investigates the existence and properties of a Bernstein–Sato functional equation in nonregular settings. In particular, we construct [Formula: see text]-modules which such formal equations can be studied. The polynomial for direct summand over field is proved this context. It observed that have zero as root, or even positive roots. Moreover, theory text]-filtrations introduced rings...

Given a JBW*-triple Z and a normal contractive projection P : Z −→ Z, we show that the (Murray-von Neumann) type of each summand of P (Z) is dominated by the type of Z.

the class of ads modules with the sip (briefly‎, ‎$sa$-modules) is studied‎. ‎various conditions for a module to be $sa$-module are given‎. ‎it is proved that for a quasi-continuous module $m$‎, ‎$m$ is a uc-module if and only if $m$ is an $sa$-module‎. ‎also‎, ‎it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...

a p–local CW–complex with H∗X a finite dimensional Fp–vector space. Then there is an integer NX (see 2.5) depending on H ∗X as a graded vector space and: (1) For p = 2, if P s t H ∗X 6= 0 for all P s t ∈ A with s < t, then X∧NX has a non–trivial stable summand Y such that H∗Y is A–free. (2) For p 6= 2, if P s t HX 6= 0 for all P s t ∈ A with s < t and QtHX 6= 0 for all Qt ∈ A, then X∧NX has a n...

Abstract Consider a reductive linear algebraic group G acting linearly on polynomial ring S over an infinite field; key examples are the general group, symplectic orthogonal and special with classical representations as in Weyl’s book: For consider direct sum of copies standard representation dual; other cases, take representation. The invariant rings respective cases determinantal rings, defin...

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.