- International Electronic Journal of Algebra
- Vol: 22 Issue: 22
- A GG NOT FH SEMISTAR OPERATION ON MONOIDS
A GG NOT FH SEMISTAR OPERATION ON MONOIDS
Authors : Ryuki Matsuda
Pages : 39-44
Doi:10.24330/ieja.325920
View : 12 | Download : 8
Publication Date : 2017-07-11
Article Type : Research
Abstract :Let $S$ be a g-monoid with quotient group q$(S)$. Let $\bar {\rm F}(S)$ (resp., F$(S)$, f$(S)$) be the $S$-submodules of q$(S)$ (resp., the fractional ideals of $S$, the finitely generated fractional ideals of $S$). Briefly, set f := f$(S)$, g := F$(S)$, h := $\bar{\rm F}(S)$, and let $\{\rm{x,y}\}$ be a subset of the set $\{$f, g, h$\}$ of symbols. For a semistar operation $\star$ on $S$, if $(E + E_1)^\star = (E + E_2)^\star$ implies ${E_1}^\star = {E_2}^\star$ for every $E \in$ x and every $E_1, E_2 \in$ y, then $\star$ is called xy-cancellative. In this paper, we prove that a gg-cancellative semistar operation need not be fh-cancellative.Keywords : Semistar operation, monoid