منابع مشابه
Whitehead Test Modules
A (right R-) module N is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module M , ExtR(M,N) = 0 implies M is projective. Dually, i-test modules are defined. For example, Z is a p-test abelian group iff each Whitehead group is free. Our first main result says that if R is a right hereditary non-right perfect ring, then the existence of p-test mo...
متن کاملWhitehead Modules over Large Principal Ideal Domains
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], ...
متن کاملOn Whitehead Precovers
It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...
متن کاملOn Generalized Whitehead Products
We define a symmetric monodical pairing G ◦ H among simply connected co-H spaces G and H with the property that S(G◦H) is equivalent to the smash product G∧H as co-H spaces. We further generalize the Whitehead product map to a map G ◦ H → G ∨ H whose mapping cone is the cartesian product. Whitehead products have played an important role in unstable homotopy. They were originally introduced [Whi...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90321-x