Volume 26, Issue 4
A Class of Left $E$-Adequate Semigroups

Commun. Math. Res., 26 (2010), pp. 289-303.

Published online: 2021-05

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• Abstract

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.

• Keywords

type $µ^+$ semigroup, abundant semigroup, left $E$-adequate semigroup, $E^+$-product.

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@Article{CMR-26-289, author = {Yonghua and Li and and 18264 and and Yonghua Li and Yong and He and and 18265 and and Yong He}, title = {A Class of Left $E$-Adequate Semigroups}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {4}, pages = {289--303}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19127.html} }
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 -

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.

YonghuaLi & YongHe. (2021). A Class of Left $E$-Adequate Semigroups. Communications in Mathematical Research . 26 (4). 289-303. doi:
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