Monadic $$k\times j$$ k × j -rough Heyting algebras
2021
In this paper, we introduce the variety of algebras, which we call monadic $$k\times j$$
-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in $$3\times 2$$
case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic $$k\times j$$
-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.
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