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Semigroup Forum

, Volume 62, Issue 1, pp 146–158 | Cite as

On the Index of Nilpotency of Semigroup Graded Rings

  • H. Gopalakrishnan
Article

Abstract

\noindent We find the index of nilpotency of a strong supplementary semilattice sum of rings, R=\tdsp\sum α∈ Y R α , where Y is a semilattice, when each R α has index of nilpotency≤ k . Then we find the index of nilpotency of R when it is graded over a rectangular band Y and each R α has index of nilpotency≤ k . These results are generalized to normal band graded rings. Further, we find sufficient conditions for a ring graded by a semilattice of nilpotent semigroups to have bounded index of nilpotency. We also show by examples that these conditions are necessary in some cases.

Keywords

Prime Ideal Nilpotent Element Regular Ring Homogeneous Element Ring Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • H. Gopalakrishnan

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