Hopfian and co-hopfian subsemigroups and extensions
نویسندگان
چکیده
This paper investigates the preservation of hopficity and co-hopficity on passing to finite-index subsemigroups and extensions. It was already known that hopficity is not preserved on passing to finite Rees index subsemigroups, even in the finitely generated case. We give a stronger example to show that it is not preserved even in the finitely presented case. It was also known that hopficity is not preserved in general on passing to finite Rees index extensions, but that it is preserved in the finitely generated case. We show that, in contrast, hopficity is not preserved on passing to finite Green index extensions, even within the class of finitely presented semigroups. Turning to co-hopficity, we prove that within the class of finitely generated semigroups, co-hopficity is preAcknowledgements: The first author’s research was funded by the European Regional Development Fund through the programme compete and by the Portuguese Government through the fct (Fundação para a Ciência e a Tecnologia) under the project pest-c/mat/ui0144/2011 and through an fct Ciência 2008 fellowship. Some of the work described in this paper was carried out while the first author was visiting Sultan Qaboos University and the authors thank the University for its support.
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تاریخ انتشار 2015