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ABSTRACT
If M and N are modules, the concept of semiregularity (and regularity) of hom(M,N) is defined and studied, and the connection with the relative direct injective- and direct projective-properties is established. The relationship of semiregularity to the Jacobson radical of hom(M,N), to the singular and cosingular ideals of hom(M,N), and to the notion of lying over or under a direct summand, is described, and the basic results in the module case are extended.
Communicated by R. Wisbauer.
ACKNOWLEDGMENTS
The authors thank Professor Wisbauer for his valuable comments on terminology and for bringing reference Kasch and Mader (Citation2004) to their attention. The first author was supported by NSERC Grant A8075, and the second author by Grant OGP 0194196. The authors are grateful to the Departments of Mathematics and Statistics at Memorial University and the University of Calgary, respectively, for their kind hospitality and financial support.
