伪草甸的一些性质

摘要：

本文的目的是研究交换的伪草甸，这是以相同的方式定义的交换草甸的结构，除了一个乘法单位的存在是不需要的。本文推广了I.~ Bethke，P.~ Rodenburg和A.~ Sevenster在他们2015年的论文中，讨论了具有1000个幂等元的交换伪草甸的情况。我们还扩展了众所周知的一般交换草甸的次直积领域的交换pseudomeadows的情况下的特征。最后，我们研究了交换伪草甸的局部化。

英文摘要：

The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I.~Bethke, P.~Rodenburg, and A.~Sevenster in their 2015 paper, to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally we investigate localizations of commutative pseudomeadows.

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