超幂零半群
Supernilpotent Semigroups
AI总结：
本文研究正则半群的幂零性、可解性与超幂零性，证明类似阿贝尔情形的直积分解结论仅在正统半群中成立，并通过反例说明非正统正则半群中该结论不成立。
摘要：
正则阿贝尔半群同构于一个阿贝尔群与一个矩形带的直积（Warne, 1994）。为了寻求正则半群的幂零性、可解性和超幂零性的类似结果，我们得到：类似的陈述仅在正统半群中成立。我们给出一个例子，表明在非正统的正则半群中同样的结论不一定成立。
英文摘要：
Regular abelian semigroups are isomorphic to a direct product of an abelian group and a rectangular band (Warne, 1994). Seeking for a similar result for nilpotency, solvability and supernilpotency of regular semigroups, we obtain that analogous statement is true only in orthodox semigroups. We provide an example that shows that the same does not have to be true in regular semigroups that are not orthodox.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
