مقاله $mathcal{R}L$- valued $f$-ring homomorphisms and lattice-valued maps

مقاله $mathcal{R}L$- valued $f$-ring homomorphisms and lattice-valued maps

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توجه : در صورت  مشاهده  بهم ريختگي احتمالي در متون زير ،دليل ان کپي کردن اين مطالب از داخل فایل ورد مي باشد و در فايل اصلي مقاله $mathcal{R}L$- valued $f$-ring homomorphisms and lattice-valued maps،به هيچ وجه بهم ريختگي وجود ندارد


بخشی از متن مقاله $mathcal{R}L$- valued $f$-ring homomorphisms and lattice-valued maps :

سال انتشار : 2017

تعداد صفحات : 30

In this paper, for each {\it lattice-valued map} $A\rightarrow L$ with some properties, a ring representation $A\rightarrow \mathcal{R}L$ is constructed. This representation is denoted by $\tau_c$ which is an $f$-ring homomorphism and a $\mathbb Q$-linear map, where its index $c$, mentions to a lattice-valued map. We use the notation $\delta_{pq}^{a}=(a -p)^{+}\wedge (q-a)^{+}$, where $p, q\in \mathbb Q$ and $a\in A$, that is nominated as {\it interval projection}. To get a well-defined $f$-ring homomorphism $\tau_c$, we need such concepts as {\it bounded}, {\it continuous}, and $\mathbb Q$-{\it compatible} for $c$, which are defined and some related results are investigated. On the contrary, we present a cozero lattice-valued map $c_{\phi}:A\rightarrow L $ for each $f$-ring homomorphism $\phi: A\rightarrow \mathcal{R}L$. It is proved that $c_{\tau_c}=c^r$ and $\tau_{c_{\phi}}=\phi$, which they make a kind of correspondence relation between ring representations $A\rightarrow \mathcal{R}L$ and the lattice-valued maps $A\rightarrow L$, Where the mapping $c^r:A\rightarrow L$ is called a {\it realization} of $c$. It is shown that $\tau_{c^r}=\tau_c$ and $c^{rr}=c^r$. Finally, we describe how $\tau_c$ can be a fundamental tool to extend pointfree version of Gelfand duality constructed by B. Banaschewski.

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مقاله $mathcal{R}L$- valued $f$-ring homomorphisms and lattice-valued maps