Finiteness properties of direct products of algebraic structures
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We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include Mal’cev algebras (including groups, rings and other classical algebras, as well as loops), idempotent algebras (including lattices), semigroups, and algebras in congruence modular varieties. We aim to identify as broad classes as possible in which the ‘expected’ preservation results ( A × B satisfies property P if and only if A and B satisfy P) hold, and to exhibit ways in which they may fail outside those classes.
Mayr , P & Ruskuc , N 2018 , ' Finiteness properties of direct products of algebraic structures ' , Journal of Algebra , vol. 494 , pp. 167-187 . https://doi.org/10.1016/j.jalgebra.2017.09.035
Journal of Algebra
© 2017, Elsevier Inc. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2017.09.035
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