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Volume 30, Issue 2
The Closed Subsemigroups of a Clifford Semigroup

Yinyin Fu & Xianzhong Zhao

Commun. Math. Res., 30 (2014), pp. 97-105.

Published online: 2021-05

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  • Abstract

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that $\{\underset{\alpha \in \overline{Y'}}{\cup} G_{\alpha} | Y' \in P(Y)\}$ is the set of all closed subsemigroups of a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$, where $\overline{Y'}$ denotes the subsemilattice of $Y$ generated by $Y'$. In particular, $G$ is the only closed subsemigroup of itself for a group $G$ and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring $\overline{P}(S)$ is isomorphic to the semiring $\overline{P}(Y)$ for a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$.

  • Keywords

semilattice, closed subsemigroup, Clifford semigroup.

  • AMS Subject Headings

16Y60, 20M07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-97, author = {Yinyin and Fu and and 18819 and and Yinyin Fu and Xianzhong and Zhao and and 18820 and and Xianzhong Zhao}, title = {The Closed Subsemigroups of a Clifford Semigroup}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {2}, pages = {97--105}, abstract = {

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that $\{\underset{\alpha \in \overline{Y'}}{\cup} G_{\alpha} | Y' \in P(Y)\}$ is the set of all closed subsemigroups of a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$, where $\overline{Y'}$ denotes the subsemilattice of $Y$ generated by $Y'$. In particular, $G$ is the only closed subsemigroup of itself for a group $G$ and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring $\overline{P}(S)$ is isomorphic to the semiring $\overline{P}(Y)$ for a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.02.01}, url = {http://global-sci.org/intro/article_detail/cmr/18973.html} }
TY - JOUR T1 - The Closed Subsemigroups of a Clifford Semigroup AU - Fu , Yinyin AU - Zhao , Xianzhong JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 105 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.13447/j.1674-5647.2014.02.01 UR - https://global-sci.org/intro/article_detail/cmr/18973.html KW - semilattice, closed subsemigroup, Clifford semigroup. AB -

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that $\{\underset{\alpha \in \overline{Y'}}{\cup} G_{\alpha} | Y' \in P(Y)\}$ is the set of all closed subsemigroups of a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$, where $\overline{Y'}$ denotes the subsemilattice of $Y$ generated by $Y'$. In particular, $G$ is the only closed subsemigroup of itself for a group $G$ and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring $\overline{P}(S)$ is isomorphic to the semiring $\overline{P}(Y)$ for a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$.

Yinyin Fu & Xianzhong Zhao. (2021). The Closed Subsemigroups of a Clifford Semigroup. Communications in Mathematical Research . 30 (2). 97-105. doi:10.13447/j.1674-5647.2014.02.01
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