ABSOLUTE CO-SUPPLEMENT AND ABSOLUTE CO-COCLOSED MODULES

作者：Tutuncu Derya Keskin^*; Toksoy Sultan Eylem

来源：Hacettepe Journal of Mathematics and Statistics, 2013, 42(1): 67-79.

• Absolute co-supplement (co-coclosed) module
• Supplement (coclosed) submodule

A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M congruent to T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0 -%26gt; A -%26gt; B -%26gt; C -%26gt; 0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.

• 出版日期2013-2