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• Author or Editor: Y. Chen
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## On Algebras and Their Radicals

Acta Mathematica Hungarica
Authors:
Y. Chen
and
K. Shum
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## Projectively condensed semigroups, generalized completely regular semigroups and projective orthomonoids

Acta Mathematica Hungarica
Authors:
Y. Chen
,
Y. He
, and
K. Shum

## Abstract

The class
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of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}\mathcal{C}$$ \end{document}
. Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}\mathcal{C}$$ \end{document}
. We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups.
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