$PMV_f$ -积代数与半低$f_u$ -环的范畴等价性
Categorical Equivalence between $PMV_f$- product algebras and semi-low $f_u$-rings
摘要：
定义了由Di Nola和Dvure $\check{c}$ enskij定义的$PMV$ -代数类的真子簇（称为$PMV_f$ -代数）与半低$f_u$ -环范畴之间的显式范畴等价.这种范畴表示是使用$MV$ -代数的素谱，通过Mundici建立的$MV$ -代数和$l_u$ -群之间的等价性，从Dubuc-Poveda方法的角度，扩展了Chang在链上定义的结构。作为特例，刻画了与布尔代数相关的半低$f_u$ -环.此外，我们还证明了一类$PMV_f$ -代数是余延的.
英文摘要：
An explicit categorical equivalence is defined between a proper subvariety of the class of $PMV$-algebras, as defined by Di Nola and Dvure$\check{c}$enskij, to be called $PMV_f$-algebras, and the category of semi-low $f_u$-rings. This categorical representation is done using the prime spectrum of the $MV$-algebras, through the equivalence between $MV$-algebras and $l_u$-groups established by Mundici, from the perspective of the Dubuc-Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low $f_u$-rings associated to Boolean algebras are characterized. Besides we show that class of $PMV_f$-algebras is coextensive.
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