Submodules of Direct Sums of Compressible Modules

Smith, P. F. and Vedadi, M. R. (2008) Submodules of Direct Sums of Compressible Modules. Communications in Algebra, 36(8), pp. 3042-3049. (doi: 10.1080/00927870802110854)

Abstract

Let R be a ring. A right R-module M is called essentially compressible if it embeds in each of its essential submodules. Also a module X-R is called completely essentially compressible if every submodule of X-R is an essentially compressible R-module. In this aricle, it is shown that a right R-module M embeds in a direct sum of compressible right R-modules if and only if M-R is essentially compressible and every nonzero essentially compressible submodule of M-R contains a compressible submodule. Every essentially compressible R-module is shown to be retractable. Moreover, if either R-R has Krull dimension, or R is Morita equivalent to a right duo ring, then a right R-module embeds in a direct sum of compressible right R-modules if and only if it is completely essentially compressible.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Smith, Professor Patrick
• Authors: Smith, P. F., and Vedadi, M. R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Communications in Algebra
• ISSN: 0092-7872