TY - CHAP
T1 - Near-Rings and Near-Fields
AU - Pilz, Günter
PY - 1996
Y1 - 1996
N2 - The fundamental facts, the structure, and some applications of near-rings and near-fields are discussed. After the fundamental definitions and examples of near-rings, near-fields are discussed, as well as their relations to group theory and to geometry. Then the structure of near-rings (semisimplicity, simplicity, primitivity) is described, and the famous density theorem is presented, along with some applications to interpolation theory. Connections to universal algebra, to the design of statistical experiments, to geometry, to group theory, and to automata theory are discussed. Finally, the relations to dynamical systems and to graph theory are mentioned.
AB - The fundamental facts, the structure, and some applications of near-rings and near-fields are discussed. After the fundamental definitions and examples of near-rings, near-fields are discussed, as well as their relations to group theory and to geometry. Then the structure of near-rings (semisimplicity, simplicity, primitivity) is described, and the famous density theorem is presented, along with some applications to interpolation theory. Connections to universal algebra, to the design of statistical experiments, to geometry, to group theory, and to automata theory are discussed. Finally, the relations to dynamical systems and to graph theory are mentioned.
UR - https://www.scopus.com/pages/publications/70350093130
U2 - 10.1016/S1570-7954(96)80017-9
DO - 10.1016/S1570-7954(96)80017-9
M3 - Chapter
SN - 0-444-82212-7
VL - 1
T3 - Handbook of Algebra
SP - 463
EP - 498
BT - Handbook of Algebra
A2 - M. Hazewinkel, null
PB - Elsevier
ER -