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<p>In this paper, generalized inverses are studied by using (one-sided) clean elements. On one hand, the (one-sided) invertibility along an element is characterized by a (one-sided) clean element. As its applications, the existence criteria for Moore–Penrose inverse, group inverse, core inverse and right core inverse are given. On the other hand, two elements being simultaneously (one-sided) invertible along a same element are characterized by a (one-sided) clean element. As its special cases, the characterizations of an element being both Moore–Penrose invertible and group invertible are given.</p>

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Characterizations of Generalized Inverses by Clean Elements

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Guiqi Shi,
  • Jianlong Chen,
  • Yukun Zhou

摘要

In this paper, generalized inverses are studied by using (one-sided) clean elements. On one hand, the (one-sided) invertibility along an element is characterized by a (one-sided) clean element. As its applications, the existence criteria for Moore–Penrose inverse, group inverse, core inverse and right core inverse are given. On the other hand, two elements being simultaneously (one-sided) invertible along a same element are characterized by a (one-sided) clean element. As its special cases, the characterizations of an element being both Moore–Penrose invertible and group invertible are given.