Geodesic
Local Near-Rings Of Cardinality P2
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 555-561

Voir la notice de l'article provenant de la source Cambridge University Press

The main result of this paper is the determination of all nonisomorphic local near-rings <N, +, •> with <N, +> =<C(p) × C(p), +> which are not near-fields. Together with the fundamental paper [6] by Zassenhaus on near-fields and the corollary to Theorem 1 of [2], this 2 paper gives a complete description of all local near-rings of order p2.We recall that a unitary near-ring N is called local if the subset L of elements in N without left inverses is an (N, N)-subgroup and N ≠ J(N). (J(N) denotes the radical of N given in [1].) In [3] it was proved that N ≠ J(N) whenever L is an ideal of N. (For previous result s concerning local near-rings we refer the reader to [3].) 
Maxson, Carlton J. Local Near-Rings Of Cardinality P2. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 555-561. doi: 10.4153/CMB-1968-066-2
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[1] 1. Beidleman, James C., A radical for near-ring modules. Mich. Math. J., 12(1965) 377-383. Google Scholar

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[4] 4. Maxson, Carlton J., On the construction of finite local near-rings (I): On non-cyclic abelian p-groups (to appear). Google Scholar

[5] 5. Zassenhaus, Hans J., The theory of groups, 2nd ed. (Chelsea, New York, 1958). Google Scholar

[6] 6. Zassenhaus, Hans J., Über endliche Fastk örper. Abh. Math. Sem., Univ. Hamburg, Vol. II (1936) 187-220. Google Scholar

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