Levels of cancellation for monoids and modules

Pere Ara, Ken Goodearl, Pace P. Nielsen, Kevin C. O'Meara, Enrique Pardo, Francesc Perera
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Abstract

Levels of cancellativity in commutative monoids $M$, determined by stable rank values in $\mathbb{Z}_{> 0} \cup \{\infty\}$ for elements of $M$, are investigated. The behavior of the stable ranks of multiples $ka$, for $k \in \mathbb{Z}_{> 0}$ and $a \in M$, is determined. In the case of a refinement monoid $M$, the possible stable rank values in archimedean components of $M$ are pinned down. Finally, stable rank in monoids built from isomorphism or other equivalence classes of modules over a ring is discussed.
单体和模块的取消等级
研究了交换单元$M$中的可取消性等级,它是由$M$元素在$mathbb{Z}_{> 0} \cup \{\infty\}$中的稳定等级值决定的。在 $k \ in\mathbb{Z}_{> 0}$ 和 $a \ in M$ 的情况下,确定了倍数 $ka$ 的稳定等级的行为。在细化单元 $M$ 的情况下,确定了 $M$ 的阿基米德成分中可能的稳定秩值。最后,讨论了由环上模块的同构等价类建立的单元的稳定秩。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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