Varieties of De Morgan monoids: minimality and irreducible algebras

0504985 - ÚI 2020 US eng V - Research Report
Moraschini, Tommaso - Raftery, J.G. - Wannenburg, J. J.
Varieties of De Morgan monoids: minimality and irreducible algebras.
Cornell University, 2018. arXiv.org e-Print archive, arXiv:1801.06650 [math.LO].
R&D Projects: GA ČR GJ15-07724Y
EU Projects: European Commission(XE) 689176 - SYSMICS
Institutional support: RVO:67985807
OECD category: Pure mathematics
https://arxiv.org/abs/1801.06650

t is proved that every finitely subdirectly irreducible De Morgan monoid A (with neutral element e) is either (i) a Sugihara chain in which e covers not(e) or (ii) the union of an interval subalgebra [not(a), a] and two chains of idempotents, (not(a)] and [a), where a = (not(e))2. In the latter case, the variety generated by [not(a), a] has no nontrivial idempotent member, and A/[not(a)) is a Sugihara chain in which not(e) = e. It is also proved that there are just four minimal varieties of De Morgan monoids. This theorem is then used to simplify the proof of a description (due to K. Swirydowicz) of the lower part of the subvariety lattice of relevant algebras. The results throw light on the models and the axiomatic extensions of fundamental relevance logics.
Permanent Link: http://hdl.handle.net/11104/0296517