TY - JOUR
T1 - 12 Cancellation modules and homogeneous idealization
AU - Ali, Majid M.
PY - 2007/11
Y1 - 2007/11
N2 - All rings are commutative with identity and all modules are unital. In this article, we characterize cancellation modules and use this characterization to give necessary and sufficient conditions for the sum and intersection of cancellation modules to be cancellation. We introduce and give some properties of the concept of [image omitted] join principal submodules. We show that via the method of idealization most questions concerning [image omitted] (weak) cancellation and [image omitted] join principal modules can be reduced to the ideal case.
AB - All rings are commutative with identity and all modules are unital. In this article, we characterize cancellation modules and use this characterization to give necessary and sufficient conditions for the sum and intersection of cancellation modules to be cancellation. We introduce and give some properties of the concept of [image omitted] join principal submodules. We show that via the method of idealization most questions concerning [image omitted] (weak) cancellation and [image omitted] join principal modules can be reduced to the ideal case.
KW - (Weak) Cancellation module
KW - 1 Join principal submodule
KW - 1(Weak) Cancellation module
KW - Idealization
KW - Multiplication module
KW - Projective module
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U2 - 10.1080/00927870701511814
DO - 10.1080/00927870701511814
M3 - Article
AN - SCOPUS:35448980666
SN - 0092-7872
VL - 35
SP - 3524
EP - 3543
JO - Communications in Algebra
JF - Communications in Algebra
IS - 11
ER -