Shift-automorphism methods for inherently nonfinitely based varieties of algebras
نویسندگان
چکیده
منابع مشابه
Inherently Nonfinitely Based Solvable Algebras
We prove that an inherently nonfinitely based algebra cannot generate an abelian variety. On the other hand, we show by example that it is possible for an inherently nonfinitely based algebra to generate a strongly solvable variety.
متن کاملInherently nonfinitely based lattices
We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational th...
متن کاملA modular inherently nonfinitely based lattice
Proof. As observed in McNulty [7], a locally finite variety V of finite type is inherently nonfinitely based if and only if for infinitely many natural numbers N , there is a non-locally-finite algebra each of whose N -generated subalgebras belongs to V. We prove the theorem by establishing these facts. We assume the reader is familiar with the basic facts of modular lattices; see [1], [2], [6]...
متن کاملRelatively Inherently Nonfinitely Q-based Semigroups
We prove that every semigroup S whose quasivariety contains a 3-nilpotent semigroup or a semigroup of index more than 2 has no finite basis for its quasi-identities provided that one of the following properties holds: • S is finite; • S has a faithful representation by injective partial maps on a set; • S has a faithful representation by order preserving maps on a chain. As a corollary it is sh...
متن کاملAutomorphism-primal algebras generate verbose varieties
A finite algebra is called automorphism-primal if its clone of term operations coincides with all operations that preserve its automorphisms. We prove that the variety generated by an automorphism-primal algebra is verbose, that is, on every member algebra, every fully invariant congruence is verbal. In [2] we discussed the notions of verbal and fully invariant congruences and examined the rela...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1989
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1989.102278