Taiwanese Journal of Mathematics

ON THE PRIME RADICAL OF A MODULE OVER A NONCOMMUTATIVE RING

Fethic Callialp and Unsal Tekir

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Abstract

Let $R$ be a ring and $M$ a left $R-$module. The radical of $M$ is the intersection of all prime submodules of $M.$ It is proved that if $R$ is a hereditary, noetherian, prime and non right artinian and $M$ a finitely generated $R-$module then the radical of $M$ has a certain form.

Article information

Source
Taiwanese J. Math., Volume 8, Number 2 (2004), 337-341.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407631

Digital Object Identifier
doi:10.11650/twjm/1500407631

Mathematical Reviews number (MathSciNet)
MR2061697

Zentralblatt MATH identifier
1059.16002

Subjects
Primary: 16E60: Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. 16D40: Free, projective, and flat modules and ideals [See also 19A13]

Keywords
prime submodule hereditary rings Noetherian rings

Citation

Callialp, Fethic; Tekir, Unsal. ON THE PRIME RADICAL OF A MODULE OVER A NONCOMMUTATIVE RING. Taiwanese J. Math. 8 (2004), no. 2, 337--341. doi:10.11650/twjm/1500407631. https://projecteuclid.org/euclid.twjm/1500407631


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