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2016•Unpublished venueRequires access

Prime Ring, Semiprime Ring and Their Connection to Quotient Ring

Rashida Pervin, Rehana Parvin, Satrajit Kumar Saha

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Abstract

A ring R is called (left) Artinian if it is Artinian as a left module over itself. In this paper, we have discussed about the prime ring, semi-prime ring and their connection to quotient ring. Mainly, we focused on A right quotient ring which is a semi-simple Artinian ring if and only if the ring is a semi-prime ring, has a finite rank and has a maximum condition on right annihilators.

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What this paper is about

A ring R is called (left) Artinian if it is Artinian as a left module over itself. In this paper, we have discussed about the prime ring, semi-prime ring and their connection to quotient ring. Mainly, we focused on A right quotient ring which is a semi-simple Artinian ring if and only if the ring is a semi-prime ring, has a finite rank and has a maximum condition on right annihilators.

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Available abstract

A ring R is called (left) Artinian if it is Artinian as a left module over itself. In this paper, we have discussed about the prime ring, semi-prime ring and their connection to quotient ring. Mainly, we focused on A right quotient ring which is a semi-simple Artinian ring if and only if the ring is a semi-prime ring, has a finite rank and has a maximum condition on right annihilators.

Key concepts: Principal ideal ring, Primitive ring, Simple ring, Reduced ring, Mathematics, Noncommutative ring, Quotient ring, Ring (chemistry)

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