TY - JOUR

T1 - Near rings without zero divisors

AU - Feigelstock, Shalom

PY - 1983/12

Y1 - 1983/12

N2 - Near rings without zero divisors, and a dual structure, near codomains, are studied. It is shown that a near ring is a near field if and only if it is an integral near ring, a near codomain, and has a non-zero distributive element. If the additive group (N, +) of a near integral domain N is cohopfian, then (N, +) possesses a fixed point free automorphism which is either torsion free or of prime order. This generalizes a well-known theorem of Ligh for finite near integral domains. A result of Ganesan [1] on the non-zero divisors in a finite ring is generalized to near rings.

AB - Near rings without zero divisors, and a dual structure, near codomains, are studied. It is shown that a near ring is a near field if and only if it is an integral near ring, a near codomain, and has a non-zero distributive element. If the additive group (N, +) of a near integral domain N is cohopfian, then (N, +) possesses a fixed point free automorphism which is either torsion free or of prime order. This generalizes a well-known theorem of Ligh for finite near integral domains. A result of Ganesan [1] on the non-zero divisors in a finite ring is generalized to near rings.

UR - http://www.scopus.com/inward/record.url?scp=34250145716&partnerID=8YFLogxK

U2 - 10.1007/bf01547797

DO - 10.1007/bf01547797

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:34250145716

SN - 0026-9255

VL - 95

SP - 265

EP - 268

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 4

ER -