ABSTRACT In this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another representation of EMV-semirings are presented by EMV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of EMV-semirings over prime ideals. Also, using the categorical equivalence between EMV-semirings and EMV-algebras, a representation of EMV-algebras are obtained.

中文翻译：

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EMV-semiring的理想

摘要 在本文中，研究了 EMV 半环及其相关 EMV 代数的同余、理想和素理想。然后对EMV-semirings进行了表征，证明了每个EMV-semirings都可以作为一个EMV-semiring嵌入到MV-semirings家族的直接产物中。此外，EMV 半环的另一种表示是由一组交换半环中连续部分的 EMV 半环表示，其茎是 EMV 半环在素理想上的定位。此外，使用 EMV-半环和 EMV-代数之间的分类等价，获得了 EMV-代数的表示。