Modules whose endomorphism rings are fusible

Motivated by fusible elements in rings, we study the concept of fusibility of endomorphisms of a module. As an application, we provide an algorithm to find left fusible decompositions of non-zero square matrices over a left fusible ring, since the algorithm given in [E. Ghashghaei and W. Wm. McGovern, Comm. Algebra, 45(3)(2017), Theorem 2.18] does not apply to find a fusible decomposition of some matrices. Furthermore, we provide various sources of examples for fusible endomorphisms. Using fusible endomorphisms, we determine conditions under which the corner ring eRe of a ring R is fusible.