×

A note on amalgams of inverse semigroups. (English) Zbl 0982.20053

Let \(I(X)\) be the inverse monoid of all partial bijections of a set \(X\). An action \(\varphi\colon I\to I(X)\) of an inverse monoid \(I\) on \(X\) is called graded if there exists a function \(p\colon X\to E(I)\) (\(E(I)\) the set of idempotents of \(I\)) such that \(\text{dom}(\varphi(e))=p^{-1}([e])\) and if \(t^{-1}t=p(x)\), then \(tt^{-1}=p(tx)\), where \([e]=\{f\in E(I),\;f\leq e\}\) and \(\varphi(t)x\) is denoted as \(tx\), \(t\in I\), \(x\in X\). Graded actions are used to find a condition for an inverse monoid to be a full amalgam of inverse semigroups; essentially all full amalgams are obtained in this way.

MSC:

20M18 Inverse semigroups
20M20 Semigroups of transformations, relations, partitions, etc.
Full Text: DOI

References:

[1] DOI: 10.1006/jabr.1996.0206 · Zbl 0858.20055 · doi:10.1006/jabr.1996.0206
[2] Steinberg, Proc. Edinburgh Math. Soc.
[3] DOI: 10.1006/jabr.1996.0025 · Zbl 0839.20076 · doi:10.1006/jabr.1996.0025
[4] Lyndon, Combinatorial group theory (1977) · Zbl 0619.20013 · doi:10.1007/978-3-642-61896-3
[5] Lawson, Inverse semigroups: The theory of partial symmetries (1999) · Zbl 1079.20505
[6] Nambooripad, Houston J. Math. 15 pp 249– (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.