Idempotent Subreducts of Semimodules over Commutative Semirings
On varieties of left distributive left idempotent groupoids
We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.
Commutative idempotent residuated lattices
We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct.
Abelian differential modes are quasi-affine
We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings.
Medial quasigroups of prime square order
We prove that, for any prime , there are precisely medial quasigroups of order , up to isomorphism.
Distributive groupoids are symmetric-by-medial: An elementary proof
We present an elementary proof (purely in equational logic) that distributive groupoids are symmetric-by-medial.
Homomorphic images of subdirectly irreducible groupoids
A groupoid is a homomorphic image of a subdirectly irreducible groupoid (over its monolith) if and only if has a smallest ideal.
Selfdistributive grupoids, Part A2: Non-idempotent left distributive quasigroups
Subdirectly irreducible non-idempotent left symmetric left distributive groupoids
We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.
Homomorphic images of finite subdirectly irreducible unary algebras
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.
Preface
Page 1