On Fully Prime Radicals

Indah Emilia Wijayanti; Dian Ariesta Yuwaningsih

doi:10.22342/jims.23.2.302.33-45

Indah Emilia Wijayanti ⁽¹⁾ , Dian Ariesta Yuwaningsih ⁽²⁾

(1) Mathematics Department Faculty of Mathematics and Natural Sciences Universitas Gadjah Mada Yogyakarta, Indonesia,

(2) Mathematics Department Faculty of Mathematics and Natural Sciences Universitas Gadjah Mada Yogyakarta

https://doi.org/10.22342/jims.23.2.302.33-45

Issue
Volume 23 Number 2 (October 2017)

Submitted
September 14, 2016

Accepted
October 31, 2017

Published
December 24, 2017

Keywords:

fully invariant submodules, fully prime submodules, fully m-system, fully prime radicals

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Abstract

In this paper we give a further study on fully prime submodules. For any fully prime submodules we define a product called $\am$-product. The further investigation of fully prime submodules in this work, i.e. the fully m-system and fully prime radicals, is related to this product. We show that the fully prime radical of any submodules can be characterize by the fully m-system. As a special case, the fully prime radical of a module $M$ is the intersection of all minimal fully prime submodules of $M$.

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Authors

Indah Emilia Wijayanti

Mathematics Department Faculty of Mathematics and Natural Sciences Universitas Gadjah Mada Yogyakarta

ind_wijayanti@ugm.ac.id (Primary Contact)

Dian Ariesta Yuwaningsih

Mathematics Department Faculty of Mathematics and Natural Sciences Universitas Gadjah Mada Yogyakarta

Wijayanti, I. E., & Yuwaningsih, D. A. (2017). On Fully Prime Radicals. Journal of the Indonesian Mathematical Society, 23(2), 33–45. https://doi.org/10.22342/jims.23.2.302.33-45