ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXVI, 2 (2007)
p. 193 - 200
On Generalized Extending Modules
M. A. Kamal and A. Sayed
Abstract.
H. Hanada, J. Kado, and K. Oshiro have introduced, in a diagram of modules
and homomorphisms, the concept of generalized M-injective modules. S.
Mohamed, and B. Mueller have given a different characterization, based on an
exchange property, of the generalized M-injective modules. Here we
introduce the concept of M-jective modules, which is a generalization of
Mohamed and Mueller concept for the generalized M-injectivity. The concept
of M-jective modules is used here to solve the problem of finding a
necessary and sufficient condition for a direct sum of extending modules to
be extending. In fact, we show that relative jectivity is necessary and
sufficient for a direct sum of two extending modules to be extending. We
also introduced the concept of generalized extending modules, and give
some properties of such modules in analougy with the known properties for
extending modules.
Keywords:
injective modules, extending modules.
AMS Subject classification: Primary: 16D50, 16D70, 16D80.
Download:
Adobe PDF 
Compressed Postscript 
Version to read:
Adobe PDF
Acta Mathematica Universitatis Comenianae
Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic
Telephone: + 421-2-60295755 Fax: + 421-2-65425882
e-Mail: amuc@fmph.uniba.sk
Internet: www.iam.fmph.uniba.sk/amuc
©
Copyright 2007, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE