On Triangulating Dimension of Rings |
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| Authors: | Gary F Birkenmeier Jae Keol Park S Tariq Rizvi |
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| Institution: | 1. Department of Mathematics , University of Louisiana at Lafayette , Lafayette, Louisiana, USA gfb1127@louisiana.edu;3. Department of Mathematics , Busan National University , Busan, South Korea;4. Department of Mathematics , Ohio State University , Lima, Ohio, USA |
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| Abstract: | For any right essential overring T of a right FI-extending ring R, it is shown that 𝒯 dim(T) ≤ 𝒯dim(R), where 𝒯dim(?) is triangulating dimension of a ring. As a consequence, we show that for a ring R the maximal right ring of quotients, Q(R), is a direct product of finitely many prime rings if and only if Q(R) is semiprime and 𝒯dim(Q(R)) is finite. Some examples which illustrate and delimit the result are provided. |
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| Keywords: | (FI-) extending Right essential overrings Triangulating dimension |
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