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1974•Canadian Journal of MathematicsOpen access

Multiplication Rings Via Their Total Quotient Rings

Malcolm P. Griffin

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Abstract

In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA. A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.

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In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA. A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.

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Available abstract

In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA. A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.

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

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