• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.865-868
• /
• 1997

Let R be a ring with a unity and let M be a unitary left R-module. In this paper, we establish [5, Proposition 2.8] by showing the proof of it. Moreover, from the above result, we obtain some properties of direct projective modules which have the summand sum property.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.557-562
• /
• 2009

A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

• The Pure and Applied Mathematics
• /
• v.6 no.1
• /
• pp.9-12
• /
• 1999

The purpose of this paper is to show that by the divisibility of a direct injective module, we obtain some results with respect to a direct injective module.

• East Asian mathematical journal
• /
• v.10 no.2
• /
• pp.261-263
• /
• 1994

• Kyungpook Mathematical Journal
• /
• v.54 no.2
• /
• pp.237-247
• /
• 2014

The purpose of this paper is to introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules. A module M is called strongly extending if each submodule of M is essential in a fully invariant direct summand of M. In this paper we examine the behavior of the class of strongly extending modules with respect to the preservation of this property in direct summands and direct sums and give some properties of these modules, for instance, strongly summand intersection property and weakly co-Hopfian property. Also such modules are characterized over commutative Dedekind domains.