On a question concerning D4-modules
2021 ◽
Vol 8
(3)
◽
pp. 467-474
An R-module M is called a D4-module if ‘whenever M1 and M2 are direct summands of M with M1 + M2 = M and M1 ∼= M2, then M1 ∩ M2 is a direct summand of M’. Let M = ⊕i∈IMi be a direct sum of submodules Mi with Hom(Mi,Mj ) = 0 for distinct i, j ∈ I. We show that M is a D4-module if and only if for each i ∈ I the module Mi is a D4-module. This settles an open question concerning direct sums of D4-modules. Our approach is independent of the solution obtained by D’Este, Keskin Tütüncü and Tribak recently.
Keyword(s):
Keyword(s):
2000 ◽
Vol 62
(1)
◽
pp. 57-66
2013 ◽
Vol 21
(1)
◽
pp. 201-208
2018 ◽
Vol 17
(08)
◽
pp. 1850155
◽
Keyword(s):
2017 ◽
Vol 60
(4)
◽
pp. 791-806
◽
Keyword(s):