We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of $r$-invertible $r$-ideals for certain ideal systems $r$) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetic phenomena with Krull monoids having infinite class group and prime divisors in all classes.

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关于理想幺半群的算术

我们研究了 Krull 和弱 Krull Mori 域的可逆理想幺半群（更准确地说，是某些理想系统 $r$ 的 $r$-可逆 $r$-理想）的代数和算术结构。我们还研究了在诺特域上至少有两个不定项的多项式环的所有非零理想的幺半群。其中，我们展示了它们不是转移 Krull，但它们与具有无限类群和所有类的素除数的 Krull 幺半群共享几个算术现象。