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<p>An element in a ring is <i>left unit-fusible</i> if it is the sum of a left zero-divisor and a unit, and a ring is <i>left unit-fusible</i> if each of its nonzero elements is left unit-fusible. We explore the relation between the unit-fusible property and (unit-) regularity. Among others, we show that every (von Neumann) regular ring is left unit-fusible, and prove a characterization theorem of the rings whose left unit-fusible elements are (von Neumann) regular.</p>

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Unit-Fusible Property via Regularity

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • P. Bhattacharjee,
  • W. Wm. McGovern,
  • Y. Zhou

摘要

An element in a ring is left unit-fusible if it is the sum of a left zero-divisor and a unit, and a ring is left unit-fusible if each of its nonzero elements is left unit-fusible. We explore the relation between the unit-fusible property and (unit-) regularity. Among others, we show that every (von Neumann) regular ring is left unit-fusible, and prove a characterization theorem of the rings whose left unit-fusible elements are (von Neumann) regular.