Planar and strongly uniform near-rings

Szeto, George

doi:10.1090/S0002-9939-1974-0340351-7

Planar and strongly uniform near-rings
HTML articles powered by AMS MathViewer

by George Szeto PDF

Proc. Amer. Math. Soc. 44 (1974), 269-274 Request permission

Abstract:

The concept of a finite strongly uniform near-ring defined by G. Ferrero is generalized to the infinite case. A relation between planar near-rings and strongly uniform near-rings is studied. A structure theorem for an integral planar near-ring of M. Anshel and J. Clay is extended to a strongly uniform nearring.

References

Michael Anshel and James R. Clay, Planar algebraic systems: Some geometric interpretations, J. Algebra 10 (1968), 166–173. MR 241473, DOI 10.1016/0021-8693(68)90092-6
Michael Anshel and James R. Clay, Planarity in algebraic systems, Bull. Amer. Math. Soc. 74 (1968), 746–748. MR 225823, DOI 10.1090/S0002-9904-1968-12025-7
James R. Clay, Generating balanced incomplete block designs from planar near rings, J. Algebra 22 (1972), 319–331. MR 306014, DOI 10.1016/0021-8693(72)90150-0
Giovanni Ferrero, Struttura degli “stems” $p$-singolari, Riv. Mat. Univ. Parma (2) 7 (1966), 243–254 (Italian, with English summary). MR 228550
Giovanni Ferrero, Stems planari e $BIB$-disegni, Riv. Mat. Univ. Parma (2) 11 (1970), 79–96 (Italian, with English summary). MR 313327
George Szeto, Finite near-rings with trivial annihilators, J. Austral. Math. Soc. 18 (1974), no. 2, 194–199. MR 0472934
George Szeto, The subsemigroups excluding zero of a near-ring, Monatsh. Math. 77 (1973), 357–362. MR 330237, DOI 10.1007/BF01300938

Über endliche Fastkörper

11

J. L. Zemmer, Near-fields, planar and non-planar, Math. Student 32 (1964), 145–150. MR 181661