TY - JOUR
T1 - The near-ring of generalized affine transformations
AU - Feigelstock, Shalom
PY - 1985/12
Y1 - 1985/12
N2 - Blackett and Wolfson studied the near-ring Aff (V) consisting of all affine transformations of a vector space V. This notion is generalized here, and the rear-ring Aff (G) consisting of affine-like maps of a nilpotent group G is introduced. The ideal structure, and the multiplication rule for Aff (G) are determined. Finally a near-ring S is introduced which generalized both Aff (G), and Gonshor's abstract affine near-rings. The ideals of S are determined.
AB - Blackett and Wolfson studied the near-ring Aff (V) consisting of all affine transformations of a vector space V. This notion is generalized here, and the rear-ring Aff (G) consisting of affine-like maps of a nilpotent group G is introduced. The ideal structure, and the multiplication rule for Aff (G) are determined. Finally a near-ring S is introduced which generalized both Aff (G), and Gonshor's abstract affine near-rings. The ideals of S are determined.
UR - http://www.scopus.com/inward/record.url?scp=84971165950&partnerID=8YFLogxK
U2 - 10.1017/S0004972700002446
DO - 10.1017/S0004972700002446
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AN - SCOPUS:84971165950
SN - 0004-9727
VL - 32
SP - 345
EP - 349
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -