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 کاملTest Groups for Whitehead Groups
We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
متن کاملAlfred North Whitehead
Alfred North Whitehead (1861-1947) never wrote a comprehensive work in philosophy of education, but he occasionally delivered lectures concerned with educational policy. These incisive talks are collected in his book The Aims of Education and Other Essays. Whitehead and Dewey were contemporaries, and their ideas are in some notable respects similar. Like Dewey, Whitehead stresses the importance...
متن کاملTest-Case Generation for Maude Functional Modules
Testing takes much of the time of the software development process, so several efforts have been devoted to automate it. We present here a tool that is able to generate test cases for Maude functional modules, and check their correctness with respect to a given specification or select a subset of these test cases to be checked by the user by using different strategies. Since these processes are...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01494-8