On Triangulating Dimension of Rings

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.

Key Words:

• (FI-) extending
• Right essential overrings
• Triangulating dimension

2000 Mathematics Subject Classification:

• Primary 16P60, 16P99
• Secondary 16S50

ACKNOWLEDGMENTS

The authors appreciate the helpful comments from Edmund Puczylowski. Also the authors are grateful for the support they received from the Mathematics Research Institute, Columbus and for the kind hospitality and support of Busan National University, the Ohio State University at Lima, and the University of Louisiana at Lafayette.

Notes

Communicated by E. R. Puczylowski.