Abstract
This paper considers near rings with d. c. c. on principalR-subgroups and a. c. c. on prinpipal annihilator right ideals. Many results concerning near rings on finite groups are then consequences of the above discussions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Clay, J. R., andJ. J. Malone: The near rings with identities on certain groups. Math. Scand.19, 146–150 (1966).
Ferrero, G.: Classificazione e costruzione degli stems p-singolari, Ist Lombardo Accad. Sci. Lett., Rend. A.102, 597–613 (1968).
Jacobson, R. A.: The structure of near rings on a group of prime order. Amer. Math. Monthly73, 59–61 (1965).
Krimmel, J.: A condition on near rings with identity. Mh. Math.77, 52–54 (1973).
Ligh, S.: On division near rings. Canad. J. Math.21, 1366–1371 (1969).
Ligh, S.: Near rings with descending chain condition. Compositio Math.21, 162–166 (1969).
Ligh, S.: Near rings with identities on certain groups. Mh. Math.75, 38–43 (1971).
Ligh, S.: D. G. near rings on certain groups. Mh. Math.75, 244–249 (1971).
Ligh, S.: On the additive groups of finite near integral domains and simple d. g. near rings. Mh. Math.76, 317–322 (1972).
Ligh, S.: A generalization of a theorem of Wedderburn. Bull. Austral. Math. Soc.8, 181–185 (1973).
Malone, J. J.: Near rings with trivial multiplication. Amer. Math. Monthly74, 1111–1112 (1967).
Szeto, C.: Finite near rings with trivial annihilators. J Austral. Math. Soc. (to appear).
Thompson, J.: Finite groups with fixed-point-free automorphisms of prime order. Proc. Nat. Acad. Sci. USA45, 578–581 (1959).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ligh, S., Ramakotaiah, D. & Reddy, Y.V. Near rings with chain conditions. Monatshefte für Mathematik 80, 119–129 (1975). https://doi.org/10.1007/BF01339080
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01339080