论文标题
注入性和投影半模块超过涉及半模型
Injective and projective semimodules over involutive semirings
论文作者
论文摘要
我们表明，MV-Algebras和MV隔离之间的术语等效性将升至涉及的残留晶格和一类称为\ textit {涉及半距离}的半度性。半度的观点可以帮助我们找到间隔$ [0,1] $的必要条件，使其成为一个涉及残留晶格的子代数。我们还将半模块理论的一些结果和技术导入了对这类半段的研究，从而概括了有关注射和投射的MV-semimodules的结果。实际上，我们注意到，这种情况起着至关重要的作用，并且每当不涉及Mundici函数时，对于参与的半度，MV隔离的结果仍然是正确的。特别是，我们证明，为了使投影性和注入性半模块重合一致是必要且充分的条件。
We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called \textit{involutive semirings}. The semiring perspective helps us find a necessary and sufficient condition for the interval $[0,1]$ to be a subalgebra of an involutive residuated lattice. We also import some results and techniques of semimodule theory in the study of this class of semirings, generalizing results about injective and projective MV-semimodules. Indeed, we note that the involution plays a crucial role and that the results for MV-semirings are still true for involutive semirings whenever the Mundici functor is not involved. In particular, we prove that involution is a necessary and sufficient condition in order for projective and injective semimodules to coincide.
