Schanuel's Lemma in P-Poor Modules

Abstract

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

The Implementation of a Rough Set of Projective Module

“…A module is projective if it is a direct sum of free modules. Furthermore, Fitriani introduces the relationship between the supplement of a module and the existence of the projective envelope of the factor module in category 𝜎[𝑀] [14], Schanuel's lemma in P-poor modules [15].…”