Planar and strongly uniform near-rings

Author:
George Szeto

Journal:
Proc. Amer. Math. Soc. **44** (1974), 269-274

MSC:
Primary 16A76

MathSciNet review:
0340351

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**Michael Anshel and James R. Clay,*Planar algebraic systems: Some geometric interpretations*, J. Algebra**10**(1968), 166–173. MR**0241473****[2]**Michael Anshel and James R. Clay,*Planarity in algebraic systems*, Bull. Amer. Math. Soc.**74**(1968), 746–748. MR**0225823**, 10.1090/S0002-9904-1968-12025-7**[3]**James R. Clay,*Generating balanced incomplete block designs from planar near rings*, J. Algebra**22**(1972), 319–331. MR**0306014****[4]**Giovanni Ferrero,*Struttura degli “stems” 𝑝-singolari*, Riv. Mat. Univ. Parma (2)**7**(1966), 243–254 (Italian, with English summary). MR**0228550****[5]**Giovanni Ferrero,*Stems planari e 𝐵𝐼𝐵-disegni*, Riv. Mat. Univ. Parma (2)**11**(1970), 79–96 (Italian, with English summary). MR**0313327****[6]**George Szeto,*Finite near-rings with trivial annihilators*, J. Austral. Math. Soc.**18**(1974), no. 2, 194–199. MR**0472934****[7]**George Szeto,*The subsemigroups excluding zero of a near-ring*, Monatsh. Math.**77**(1973), 357–362. MR**0330237****[8]**H. Zassenhaus,*Über endliche Fastkörper*, Abh. Math. Sem. Univ. Hamburg**11**(1936), 187-220.**[9]**J. L. Zemmer,*Near-fields, planar and non-planar*, Math. Student**32**(1964), 145–150. MR**0181661**

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0340351-7

Keywords:
Equivalent multipliers,
near-rings,
integral planar near-rings,
planar near-rings,
strongly uniform near-rings

Article copyright:
© Copyright 1974
American Mathematical Society