Associative rings with large center

D. V. Zlydnev

M. V. Lomonosov Moscow State University

Abstract: 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 $I\lhd R$ such that $I$ is not a ring with large center.

UDC: 512.552.3+512.552.4

 English version: Journal of Mathematical Sciences (New York), 2013, 191:5, 691–693

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