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引用次数: 0
摘要
我们引入了具有无穷大的 PC 可取消加法单元的概念，并用它来描述具有无穷大的可取消加法主理想域。我们的表征改进了文献中的各种已知表征，既包括换元可消加性单元的表征，也包括换元环理论中的类似表征。
We introduce the notion of PC cancellative additive monoids with infinity and use it to characterize cancellative additive principal ideal domains with infinity. Our characterization improves various known characterizations from the literature, both, in the context of the commutative cancellative monoids, as well as in the context of the analogues of the statements from the commutative ring theory.
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Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc.
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