We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.’s of size ≥ א2 have nonfree Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if ExtR(M,R) = 0. The second author proved that the problem of whether every Whitehead Z-module is free is independent of ZFC + GCH (cf. [5], ...

The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. limit this procedure, called asymptotic product, provides a homological counterpart Buchweitz's construction stable cohomology. resulting connected sequence functors isomorphic Triulzi's J-completion Tor functor. A comparison map from Vogel homology constructed and show...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

in the present study, a simple and sensitive extractive spectrophotometric method is described for determination of buspirone. the method is based on the reaction of buspirone and bromocresol green. the ion-pair complex was quantitatively extracted into chloroform at ph 2.3 followed by spectrophotometric determination at 415 nm. the complex was stable up to 2 days and obeyed beer's law over the...

a simple and sensitive extractive spectrophotometric method is described for determination of tropicamide. the method is based on the reaction of tropicamide and bromocresol green. the ion-paired colored complex was extracted with chloroform at ph 3. the extracted complex showed maximum absorbance at 423 nm. the complex was stable up to 2 days and obeyed beer's law over the concentration r...