Varieties of BL-algebras
نویسندگان
چکیده
In this paper we overview recent results about the lattice of subvarieties of the variety BL of BL-algebras and the equational definition of some families of them.
منابع مشابه
FREE ALGEBRAS IN VARIETIES OF BL-ALGEBRAS GENERATED BY A BLn-CHAIN
Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of Ln and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the...
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A generalized BL-algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities x ∧ y = ((x ∧ y)/y)y = y(y\(x∧ y)). It is shown that all finite GBL-algebras are commutative, hence they can be constructed by iterating ordinal sums and direct products of Wajsberg hoops. We also observe that the idempotents in a GBL-algebra form a subalgebra of elements that commute with ...
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عنوان ژورنال:
- Soft Comput.
دوره 9 شماره
صفحات -
تاریخ انتشار 2005