Codivisible and Projective Covers
作者:
Mark L. Teply,
期刊:
Communications in Algebra
(Taylor Available online 1974)
卷期:
Volume 1,
issue 1
页码: 23-38
ISSN:0092-7872
年代: 1974
DOI:10.1080/00927877408548607
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
This paper continues the study of codivisible modules, whose definition is a “dualization” of Lambek's concept [4] of a divisible module relative to a torsion theory. The main purpose of this work is to give a solution to the following problem posed by Bland [2]: “It would be interesting to know under what conditions the universal existence of codivisible covers implies that of projective covers.” The if-and-only-if nature of the solution, which is given in Theorems 2 and 4, shows that our sufficient conditions are “best possible” conditions. The method of the solution introduces the concept of a pseudo-hereditary torsion theory, which may be of interest in its own right; in particular, every hereditary torsion theory and every faithful torsion theory is pseudo-hereditary. The main results for a pseudo-hereditary torsion theory (T, F) relate the conditions, R/T(R) is semiperfect and R/T(R) is left perfect, to the existence of codivisible covers (see Theorems 1 and 3 and Corollaries 1 and 2).
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