Noetherian, artinian, and semisimple modules and rings

1967 ◽  
pp. 51-57
Author(s):  
Carl Faith
Keyword(s):  
Semisimple Modules

Structure of virtually semisimple modules over commutative rings

2020 ◽  
Vol 48 (7) ◽  
pp. 2872-2882
Author(s):  
M. Behboodi ◽  
A. Daneshvar ◽  
M. R. Vedadi
Keyword(s):  
Commutative Rings ◽  
Semisimple Modules

Generalized Co-Semisimple Modules

1990 ◽  
Vol 18 (12) ◽  
pp. 4235-4253
Author(s):  
Robert Wisbauer
Keyword(s):  
Semisimple Modules

T-Semisimple Modules and T-Semisimple Rings

2013 ◽  
Vol 41 (5) ◽  
pp. 1882-1902 ◽  
Author(s):  
Sh. Asgari ◽  
A. Haghany ◽  
Y. Tolooei
Keyword(s):  
Semisimple Modules

scholarly journals Virtually semisimple modules and a generalization of the Wedderburn-Artin theorem

2017 ◽  
Vol 46 (6) ◽  
pp. 2384-2395 ◽  
Author(s):  
Mahmood Behboodi ◽  
Asghar Daneshvar ◽  
M. R. Vedadi
Keyword(s):  
Semisimple Modules

scholarly journals Schanuel's Lemma in P-Poor Modules

2019 ◽  
Vol 5 (2) ◽  
pp. 76-82
Author(s):  
Iqbal Maulana
Keyword(s):  
Linear Algebra ◽  
Projective Module ◽  
Vector Spaces ◽  
Projective Modules ◽  
Module Theory ◽  
Semisimple Modules ◽  
Special Case

Modules are a generalization of the vector spaces of linear algebra in which the “scalars” are allowed to be from a ring with identity, rather than a field. In module theory there is a concept about projective module, i.e. a module over ring R in which it is projective module relative to all modules over ring R. Next, there is the fact that every module over ring R is projective module relative to all semisimple modules over ring R. If P is a module over ring R which it’s projective relative only to all semisimple modules over ring R, then P is called p-poor module. In the discussion of the projective module, there is a lemma associated with the equivalence of two modules K1 and K2 provided that there are two projective modules P1 and P2 such that is isomorphic to . That lemma is known as Schanuel’s lemma in projective modules. Because the p-poor module is a special case of the projective module, then in this paper will be discussed about Schanuel’s lemma in p-poor modules

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