non-regularity of multiplications for general measure algebras

let $fm(x)$ be the  space of  all finite regular borel measures on $x$. a general measure algebra is a subspace  of$fm(x)$,which is an $l$-space and has a multiplication preserving the probability measures. let $clsubseteqfm(x)$ be a general measure algebra on a locallycompact space $x$. in this paper, we investigate the relation between arensregularity of $cl$ and the topology of $x$. we  find conditionsunder which the arens regularity of $fl$ implies the compactness of $x$.weshow that these conditions are necessary.we also  present some examples in showing that the new conditions aredifferent from  theorem 3.1 of cite{7}.