Homomorfisa Modul Deret Pangkat Tergeneralisasi Miring

Ahmad Faisol; Fitriani Fitriani

doi:10.24198/jmi.v17.n2.34646.119-126

Homomorfisa Modul Deret Pangkat Tergeneralisasi Miring

Ahmad Faisol, Fitriani Fitriani

Abstract

Diberikan sebarang ring komutatif $R$ dengan elemen satuan, monoid terurut tegas $(S,\leq)$, homomorfisma monoid $\omega:S\rightarrow End(R)$, submonoid $S_1,S_2\subseteq S$ yang masing-masing dilengkapi urutan $\leq_1, \leq_2$ yang \textit{coarser} terhadap urutan $\leq$ pada $S$, dan modul $M_1,M_2$ atas $R$. Pada penelitian ini, dikonstruksi modul deret pangkat tergeneralisasi miring $M_1[[S_1,\leq_1,\omega]]$ dan $M_2[[S_2,\leq_2,\omega]]$ atas ring deret pangkat tergeneralisasi miring $R[[S,\leq,\omega]]$. Selain itu, dibuktikan pemetaan $\tau$ dari $M_1[[S_1,\leq_1,\omega]]$ ke $M_2[[S_2,\leq_2,\omega]]$ dengan $\tau(\alpha_1)=\gamma\circ\alpha_1\circ\delta^{-1}$ merupakan $R[[S,\leq,\omega]]$-homomorfisma modul dengan mensyaratkan $f(\delta^{-1}(u))=f(u)$ dan $\omega_{\delta^{-1}(v)}=\omega_{v}$ untuk setiap $u,v\in S_2$ dan $f\in R[[S,\leq,\omega]]$.

Keywords

monoid terurut tegas, homomorfisma ring, ring deret pangkat tergeneralisasi miring, homomorfisma modul, modul deret pangkat tergeneralisasi miring.

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References

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DOI: https://doi.org/10.24198/jmi.v17.n2.34646.119-126