Axiomatizability of the class of subdirectly irreducible acts over an Abelian group

2020 ◽  
Vol 59 (5) ◽  
pp. 582-593
Author(s):  
A. A. Stepanova ◽  
D. O. Ptakhov
Keyword(s):  
Abelian Group ◽  
Subdirectly Irreducible

scholarly journals The additive groups of subdirectly irreducible rings

1979 ◽  
Vol 20 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Shalom Feigelstock
Keyword(s):  
Abelian Group ◽  
Additive Group ◽  
Subdirectly Irreducible ◽  
Torsion Free

An abelian group G is said to be subdirectly irreducible if there exists a subdirectly irreducible ring R with additive group G. If G is subdirectly irreducible, and if every ring R with additive group G, and R2 ≠ 0, is subdirectly irreducible, then G is said to be strongly subdirectly irreducible. The torsion, and torsion free, subdirectly irreducible and strongly subdirectly irreducible groups are classified completely. Results are also obtained concerning mixed subdirectly irreducible and strongly subdirectly irreducible groups.

scholarly journals On the additive groups of subdirectly irreducible rings

1986 ◽  
Vol 34 (2) ◽  
pp. 275-281 ◽  
Author(s):  
Yasuyuki Hirano ◽  
Isao Mogami
Keyword(s):  
Abelian Group ◽  
Group Structure ◽  
Additive Group ◽  
Subdirectly Irreducible ◽  
Torsion Free

In this paper we study the additive group structure of subdirectly irreducible rings and their hearts. We give and example of a torsion-free, non-reduced abelian group which is not the underlying additive group of any associative subdirectly irreducible ring. It is a counterexample to a theorem in Feigelstock's book “Additive Groups of Rings.”

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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