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*p-MODULES AND A SPECIAL CLASS OF MODULES DETERMINED BY THE ESSENTIAL CLOSURE OF THE CLASS OF ALL *-RINGS

Prasetyo, Puguh Wahyu and Wijayanti, Indah Emilia and France-Jackson, Halina (2017) *p-MODULES AND A SPECIAL CLASS OF MODULES DETERMINED BY THE ESSENTIAL CLOSURE OF THE CLASS OF ALL *-RINGS. [Artikel Dosen]

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Abstract

A ring A is called a *-ring if A is a prime ring and A has no nonzero proper prime homomorphic image. The *-ring was introduced by Korolczuk in 1981. Since *-rings have an important role in radical theory of rings, the properties of *-ring have been being investigated intensively. Since every ring can be viewed as a module over itself, the generalization of *-ring into module theory is an interesting investigation. We would like to present the generalization of *-rings in module theory named *p-modules. An A-module M is called a -module if M is a prime A-module and M has no nonzero proper prime submodule. According to the result of our investigation, we show that every *-ring is a *p-module over itself. Furthermore, let A be a ring, let M be an A-module, and let I be an ideal of A with I subset (0:M)A where (0:M)A={a in A| aM={0}}. We show that M is a *p-module over A if and only if M is a *p-module over A/I. On the other hand, the essential closure *k of the class of all *-rings is a special class of rings. As the last result of our investigation, we present the special class of modules determined by *k.

Item Type: Artikel Dosen
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisi / Prodi: Faculty of Teacher Training and Education (Fakultas Keguruan dan Ilmu Pendidikan) > S1-Mathematics Education (S1-Pendidikan Matematika)
Depositing User: puguh prasetyo
Date Deposited: 09 Aug 2019 03:55
Last Modified: 09 Aug 2019 03:55
URI: http://eprints.uad.ac.id/id/eprint/14349

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