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On the Index of Nilpotency of Semigroup Graded Rings

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.

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Gopalakrishnan, H. On the Index of Nilpotency of Semigroup Graded Rings . Semigroup Forum 62, 146–158 (2001). https://doi.org/10.1007/s002330010027

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  • DOI: https://doi.org/10.1007/s002330010027

Keywords

  • Prime Ideal
  • Nilpotent Element
  • Regular Ring
  • Homogeneous Element
  • Ring Homomorphism