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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 2, Pages 321-326

Chain Conditions on Semirings

Received 4 May 1994; Revised 7 January 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we characterize the class of semirings S for which the semirings of square matrices Mn(S) over S are (left) k-artinian. Also an analogue of the Hilbert basis theorem for semirings is obtained.