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On inverse categories with split idempotents

Emil Schwab, Emil Daniel Schwab (2015)

Archivum Mathematicum

We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.

On left C - 𝒰 -liberal semigroups

Yong He, Fang Shao, Shi-qun Li, Wei Gao (2006)

Czechoslovak Mathematical Journal

In this paper the equivalence 𝒬 ˜ U on a semigroup S in terms of a set U of idempotents in S is defined. A semigroup S is called a 𝒰 -liberal semigroup with U as the set of projections and denoted by S ( U ) if every 𝒬 ˜ U -class in it contains an element in U . A class of 𝒰 -liberal semigroups is characterized and some special cases are considered.

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