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<p>Different kinds of decompositions of a square matrix have been studied in the literature by altering the conditions on the summands of core-nilpotent decomposition. Motivated by the observation that for an element from an associative ring the Drazin inverse and the core-nilpotent decomposition coexist, and many of among the techniques which are useful in the case of matrices fail in the case dealing with the elements from an associative ring, the theory of generalized inverse and the minus partial order are used to characterize and study the generalized core-nilpotent decomposition of an element from an associative ring.</p>

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Generalized Core-nilpotent Decomposition of Ring Elements

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Savitha Varkady,
  • Umashankara Kelathaya,
  • Manjunatha Prasad Karantha

摘要

Different kinds of decompositions of a square matrix have been studied in the literature by altering the conditions on the summands of core-nilpotent decomposition. Motivated by the observation that for an element from an associative ring the Drazin inverse and the core-nilpotent decomposition coexist, and many of among the techniques which are useful in the case of matrices fail in the case dealing with the elements from an associative ring, the theory of generalized inverse and the minus partial order are used to characterize and study the generalized core-nilpotent decomposition of an element from an associative ring.