Full subrings of E-rings

Shalom Feigelstock

doi:10.1017/s0004972700017731

Full subrings of E-rings

Shalom Feigelstock

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A ring R is said to be an E-ring if the map R → E(R⁺), of R into the ring of endomorphisms of its additive group via a → a₁ = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group R₁ of left multiplication maps by elements of R, is a full subgroup of E(R⁺)⁺ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of S-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R⁺) is an E-ring, and E(R⁺)⁺ /R₁ is bounded. Some results concerning additive groups of TE-rings will be obtained.

Original language	English
Pages (from-to)	275-280
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	54
Issue number	2
DOIs	https://doi.org/10.1017/s0004972700017731
State	Published - Oct 1996

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abstract = "A ring R is said to be an E-ring if the map R → E(R+), of R into the ring of endomorphisms of its additive group via a → a1 = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group R1 of left multiplication maps by elements of R, is a full subgroup of E(R+)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of S-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ /R1 is bounded. Some results concerning additive groups of TE-rings will be obtained.",

author = "Shalom Feigelstock",

year = "1996",

month = oct,

doi = "10.1017/s0004972700017731",

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N2 - A ring R is said to be an E-ring if the map R → E(R+), of R into the ring of endomorphisms of its additive group via a → a1 = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group R1 of left multiplication maps by elements of R, is a full subgroup of E(R+)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of S-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ /R1 is bounded. Some results concerning additive groups of TE-rings will be obtained.

AB - A ring R is said to be an E-ring if the map R → E(R+), of R into the ring of endomorphisms of its additive group via a → a1 = left multiplication by a, is an isomorphism. In this note torsion free rings R for which the group R1 of left multiplication maps by elements of R, is a full subgroup of E(R+)+ will be considered. These rings are called TE-rings. It will be shown that TE-rings satisfy many properties of S-rings, and that unital TE-rings are E-rings. If R is a TE-ring, then E(R+) is an E-ring, and E(R+)+ /R1 is bounded. Some results concerning additive groups of TE-rings will be obtained.

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Full subrings of E-rings

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