SIFAT-SIFAT SUBMODUL PRIMA GABUNGAN PADA (R,S)-MODUL; PROPERTIES OF JOINTLY PRIME SUBMODULES ON (R,S)-MODULES

Dian Ariesta Yuwaningsih, Indah Emilia Wijayanti

2013 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

Let R and S be arbitrary rings. An additive abelian group M is called an (R; S)-bimodule if M is a left R-module, a right S-module, and satisfies the compatibility condition, that is r(ms) = (rm)s for all r 2 R, m 2 M, dan s 2 S. This compatibility property can’t always be fulfilled, although an additive abelian group M is a left R-module and also a right S-module. This condition that underlying the definition of (R; S)-modules. Furthermore, there are many ways to define prime submodules on (R; S)-modules. We focus on jointly prime (R; S)-submodules. In this thesis, we present some properties of a jointly prime (R; S)-submodule. Moreover, we also define a jointly prime radical on (R; S)-modules and present its properties

Kata Kunci : Prima gabungan; Modul