论文标题
正确产生的正确理想的半群
Semigroups whose right ideals are finitely generated
论文作者
论文摘要
如果有限地生成$ s $的每一个正确的理想，我们将Noetherian弱的Semigroup $ s $ s $ noetherian称为noetherian；同等地，$ s $满足正确理想的上升链条条件。我们在主权理想方面提供了弱正确的Noetherian的财产的等效表述，并且我们还根据其行为来表征弱正确的Noetherian noeterian单型。 我们调查了在商，子群和各种半群理论结构下弱的noetherian属性的行为。特别是，我们发现两个半群的直接乘积是弱右noetherian的必要条件。我们根据其同性恋者来表征弱的noetherian常规半群。我们还发现，对于完全简单的半群的强大半杂志，我们发现了必要和足够的条件，即弱的noetherian。最后，我们证明，当且仅当$ s/\ mathcal {h} $有限地生成时，具有有限的许多Archimedean组件的交换性semigroup $ s $是弱（右）Noetherian的。
We call a semigroup $S$ weakly right noetherian if every right ideal of $S$ is finitely generated; equivalently, $S$ satisfies the ascending chain condition on right ideals. We provide an equivalent formulation of the property of being weakly right noetherian in terms of principal right ideals, and we also characterise weakly right noetherian monoids in terms of their acts. We investigate the behaviour of the property of being weakly right noetherian under quotients, subsemigroups and various semigroup-theoretic constructions. In particular, we find necessary and sufficient conditions for the direct product of two semigroups to be weakly right noetherian. We characterise weakly right noetherian regular semigroups in terms of their idempotents. We also find necessary and sufficient conditions for a strong semilattice of completely simple semigroups to be weakly right noetherian. Finally, we prove that a commutative semigroup $S$ with finitely many archimedean components is weakly (right) noetherian if and only if $S/\mathcal{H}$ is finitely generated.
