Inherently Nonfinitely Based Solvable Algebras
نویسندگان
چکیده
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.
منابع مشابه
Slim Groupoids
Slim groupoids are groupoids satisfying x(yz) ≈ xz. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such g...
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 کاملEquational Complexity of the Finite Algebra Membership Problem
We associate to each variety of algebras of finite signature a function on the positive integers called the equational complexity of the variety. This function is a measure of how much of the equational theory of a variety must be tested to determine whether a finite algebra belongs to the variety. We provide general methods for giving upper and lower bounds on the growth of equational complexi...
متن کاملOn Finitely Based Groups and Nonfinitely Based Quasivarieties
We define the notion of strictly finitely based varieties of groups, and determine which finite groups are strictly finitely based. Then we use this result to prove the existence of ‘very nonfinitely based’ finite algebras, thereby solving two open problems in the theory of quasivarieties.
متن کاملSolvable Lie algebras with $N(R_n,m,r)$ nilradical
In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008