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1975•Canadian Mathematical BulletinOpen access

On Ring Properties of Injective Hulls

Norman Lang

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Abstract

Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense. It is known that is a regular ring (in the sense of von Neumann) if and only if the singular ideal of R is zero.

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Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense. It is known that is a regular ring (in the sense of von Neumann) if and only if the singular ideal of R is zero.

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Available abstract

Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense. It is known that is a regular ring (in the sense of von Neumann) if and only if the singular ideal of R is zero.

Key concepts: Mathematics, Ring (chemistry), Multiplication (music), Injective function, Principal ideal ring, Hull, Ideal (ethics), Associative property

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