TY - JOUR

T1 - Full subrings of E-rings

AU - Feigelstock, Shalom

PY - 1996/10

Y1 - 1996/10

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.

UR - http://www.scopus.com/inward/record.url?scp=0030266250&partnerID=8YFLogxK

U2 - 10.1017/s0004972700017731

DO - 10.1017/s0004972700017731

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AN - SCOPUS:0030266250

SN - 0004-9727

VL - 54

SP - 275

EP - 280

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -