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Semidirect products and crossed modules in monoids with operations

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We describe actions, semidirect products and crossed modules in categories of monoids with operations. Moreover we characterize, in this context, the internal categories corresponding to crossed modules. Concrete examples in the cases of monoids, semirings and distributive lattices are given.

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Nelson Martins-Ferreira, Andrea Montoli, Manuela Sobral, Semidirect products and crossed modules in monoids with operations, Journal of Pure and Applied Algebra, Volume 217, Issue 2, 2013, Pages 334-347, ISSN 0022-4049, https://doi.org/10.1016/j.jpaa.2012.06.022.

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