Algebra and Logic
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The Computational Power of Infinite Time Blum–Shub–Smale Machines
Algebra and Logic - Tập 56 - Trang 37-62 - 2017
Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM)
are characterized via iterated Turing jumps, and we propose a normal form for
these functions. It is also proved that the set of ITBM computable reals
coincides with ℝ∩L ωω.
Criterion for Invertibility of Endomorphisms and Test Rank of Metabelian Products of Abelian Groups
Algebra and Logic - Tập 43 - Trang 316-326 - 2004
Let G be a finitely generated torsion-free group, which is a metabelian product
of Abelian groups. We establish a criterion for endomorphisms satisfying some
extra restriction to be invertible in G. Test sets for IA-endomorphisms of G are
described and its test rank computed.
Locally finitely approximable and locally representable varieties of algebras
Algebra and Logic - Tập 16 - Trang 1-16 - 1977
Dominions in Solvable Groups
Algebra and Logic - - 2015
The dominion of a subgroup H of a group G in a class M is the set of all
elements a ∈ G whose images are equal for all pairs of homomorphisms from G to
each group in M that coincide on H. A group H is absolutely closed in a class M
if, for any group G in M and any inclusion H ≤ G, the dominion of H in G (with
respect to M) coincides with H (i.e., H is closed in G). We prove that every
torsion-free...
Uniformization in Superstructures Over Some Extensions of ℝ
Algebra and Logic - Tập 54 - Trang 273-278 - 2015
The uniformization theorem for Σ-predicates in a hereditarily finite
superstructure over the real exponential field proved in [1] is generalized to
the case of an arbitrary Σ- predicate P ⊆ ℍ $$ \mathbb{W} $$ (ℝ exp ) ×ℍ $$
\mathbb{W} $$ (ℝ exp )....
Local finiteness of certain groups with minimum condition for Abelian subgroups
Algebra and Logic - - 1977
Lattices of subgroup and subsystem functors
Algebra and Logic - Tập 45 - Trang 403-414 - 2006
Lattices of subgroup and subsystem functors are investigated. In particular, it
is proved that for the case where X is a formation of finite groups and width of
the lattice F0(X) is at most |π(X)|, the formation X is metanilpotent and |π(X)|
⩽ 3.
Product varieties of m-groups
Algebra and Logic - Tập 51 - Trang 479-486 - 2013
A new concept of mimicking is introduced. We point out representations that
mimic a variety $$ \mathcal{A} $$ of Abelian m-groups and a variety $$
\mathcal{J} $$ of m-groups defined by an identity x* = x-1. It is proved that if
a variety $$ \mathcal{U} $$ of m-groups is generated by some class of m-groups,
and a variety $$ \mathcal{V} $$ of m-groups is mimicked by some class of
m-groups, then thei...
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