‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

The external validity of artificial "trivial" laboratory settings is examined. Past views emphasizing generalizability of relations among conceptual variables are reviewed and affirmed, One major implication of typical challenges to the external validity of l ratory arch t ed wi h gression r search: If l borat ry es a ch ow n external validity, then laboratory studies should fail to detect rela...

In papers by Semmes [6], Macpherson and Neumann [4] and Brazil, Covington, Penttila, Praeger and Woods [2], it has been shown that stabilizers of filters (equivalently, stabilizers of ideals) play a crucial role in the study of maximal subgroups of infinite symmetric groups. Semmes proved that if if is a maximal subgroup of S = Sym (Q), where Q is a set of infinite cardinality K and H contains ...

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...

Perturbative study of many quantum field models has lead to many impressive results: beta functions for QED and for the Φ4 theory are known up to the fifth order whereas that of QCD up to the fourth order [1]-[7]. These studies however are based on the expansion in the small coupling constant such that the behavior at large couplings is completely missed. Although the possibility of a perturbat...