TY - JOUR
T1 - A Class of Left $E$-Adequate Semigroups
AU - Li , Yonghua
AU - He , Yong
JO - Communications in Mathematical Research 
VL - 4
SP - 289
EP - 303
PY - 2021
DA - 2021/05
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19127.html
KW - type $µ^+$ semigroup, abundant semigroup, left $E$-adequate semigroup, $E^+$-product.
AB - <p style="text-align: justify;">In this paper we establish a construction of a class of left $E$-adequate
semigroups by using semilattices of cancellative monoids and fundamental left $E$-adequate semigroups. We first introduce concepts of type $µ^+$ ($µ^∗$, $µ$) abundant
semigroups and type $µ^+$ left $E$-adequate semigroups. In fact, regular semigroups are
type $µ^+$ abundant semigroups and inverse semigroups are type $µ^+$ left $E$-adequate
semigroups. Next, we construct a special kind of algebras called $E^+$-product. It is
proved that every $E^+$-product is a type $µ^+$ left $E$-adequate semigroup, and every
type $µ^+$ left $E$-adequate semigroup is isomorphic to an $E^+$-product of a semilattice
of cancellative monoids with a fundamental left $E$-adequate semigroup. Finally, as a
corollary of the main result, it is deduced that every inverse semigroup is isomorphic
to an $E^+$-product of a Clifford semigroup by a fundamental inverse semigroup.</p>