FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 4, PAGES 141-144

Associative rings with large center

D. V. Zlydnev

Abstract

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A ring $R$ is called a ring with large center if any nonzero ideal of $R$ has nonzero intersection with the center of $R$. We give some conditions for an ideal of a ring with large center to be itself a ring with large center, and also we provide an example of a ring with large center $R$ and its ideal $\$\; I\; \backslash lhd\; R\; \$$ such that $I$ is not a ring with large center.

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Last modified: July 2, 2012