Definable principal congruences and solvability
نویسندگان
چکیده
We prove that in a locally finite variety that has definable principal congruences (DPC), solvable congruences are nilpotent, and strongly solvable congruences are strongly abelian. As a corollary of the arguments we obtain that in a congruence modular variety with DPC, every solvable algebra can be decomposed as a direct product of nilpotent algebras of prime power size.
منابع مشابه
ar X iv : m at h / 96 07 22 9 v 1 [ m at h . R A ] 1 J ul 1 99 6 Self – Rectangulating Varieties of Type 5
We show that a locally finite variety which omits abelian types is self–rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type–set {5 }. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the ...
متن کاملSelf-Rectangulating Varieties of Type 5
We show that a locally finite variety which omits abelian types is self–rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type–set {5 }. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the ...
متن کاملRelation Formulas for Protoalgebraic Equality Free Quasivarieties; Pałasińska's Theorem Revisited
We provide a new proof of the following Pa lasińska’s theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are Q-relation formulas, for a protoalgebraic equality free quasivariety Q, which are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Havi...
متن کاملVarieties with Definable Factor Congruences
We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are definable in a first-orderlogic sense, among them the concept of Definable Factor Congruences (DFC). The main results are that DFC is a Mal’cev property and that it is equivalent to all other conditions formulated; in particular we prove that V has DFC if and...
متن کاملSolvability of an impulsive boundary value problem on the half-line via critical point theory
In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 157 شماره
صفحات -
تاریخ انتشار 2009