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Abstract
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In this paper we continue our investigation of Wold-type
decomposition in Baer ∗-rings. We obtain further information
on building blocks of commuting pairs of isometries, by
constructing Popovici decomposition of bi-isometries in Baer
∗-rings. Then we introduce Suciu decomposition of an Abelian
isometric semigroup. Moreover, we clarify the relationship
between the Wold-Slocinski’s decomposition of a given biisometry and Suciu decomposition of the semigroup induced
by this bi-isometry
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