A GG NOT FH SEMISTAR OPERATION ON MONOIDS

Authors : Ryuki MATSUDA

Pages : 39-44

Doi:10.24330/ieja.325920

View : 13 | Download : 11

Publication Date : 2017-07-11

Article Type : Research Paper

Abstract :Let  $S$  be a  g-monoid with quotient group  q$insert ignore into journalissuearticles values(S);$. Let  $\bar {\rm F}insert ignore into journalissuearticles values(S);$ insert ignore into journalissuearticles values(resp., F$insert ignore into journalissuearticles values(S);$, f$insert ignore into journalissuearticles values(S);$);  be the  $S$-submodules of  q$insert ignore into journalissuearticles values(S);$ insert ignore into journalissuearticles values(resp., the  fractional ideals of  $S$,  the finitely generated  fractional ideals of $S$);. Briefly, set  f := f$insert ignore into journalissuearticles values(S);$, g := F$insert ignore into journalissuearticles values(S);$, h := $\bar{\rm F}insert ignore into journalissuearticles values(S);$, and let   $\{\rm{x,y}\}$  be a subset of the set  $\{$f, g, h$\}$  of symbols. For a semistar operation  $\star$ on  $S$, if  $insert ignore into journalissuearticles values(E + E_1);^\star = insert ignore into journalissuearticles values(E + E_2);^\star$ 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