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The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative $π$ -group), is introduced. Commutative $π$ -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...

Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris

Jaroslav Guričan (1993)

Commentationes Mathematicae Universitatis Carolinae

The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.

Homomorphic correspondences of relational systems

František Krutský (1983)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Homomorphic images of subdirectly irreducible groupoids

David Stanovský (2001)

Commentationes Mathematicae Universitatis Carolinae

A groupoid $H$ is a homomorphic image of a subdirectly irreducible groupoid $G$ (over its monolith) if and only if $H$ has a smallest ideal.

Homomorphisms between $A$ -projective Abelian groups and left Kasch-rings

Ulrich F. Albrecht, Jong-Woo Jeong (1998)

Czechoslovak Mathematical Journal

Glaz and Wickless introduced the class $G$ of mixed abelian groups $A$ which have finite torsion-free rank and satisfy the following three properties: i) $A_{p}$ is finite for all primes $p$ , ii) $A$ is isomorphic to a pure subgroup of $Π_{p} A_{p}$ , and iii) $H o m (A, t A)$ is torsion. A ring $R$ is a left Kasch ring if every proper right ideal of $R$ has a non-zero left annihilator. We characterize the elements $A$ of $G$ such that $E (A) / t E (A)$ is a left Kasch ring, and discuss related results.

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Chong-Guang Cao, Xian Zhang (2002)

Archivum Mathematicum

Let $M_{n}$ be the multiplicative semigroup of all $n \times n$ complex matrices, and let $U_{n}$ and $G L_{n}$ be the $n$ –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from $U_{n}$ to $G L_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ , and thereby determine multiplicative homomorphisms from $U_{n}$ to $M_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ . This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if $f : U_{n} \to M_{n}$ is a spectrum–preserving multiplicative homomorphism, then there exists a matrix $R$ in $G L_{n}$ such that $f (A) = R A R$ for...

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Homology Stability for GLn of a Dedekind Domain.

Homology Stability for Linear Groups.

Homology stability for orthogonal groups over algebraically closed fields

Homology stability for outer automorphism groups of free groups.

Homology stability for the special linear group of a field and Milnor-Witt $K$ -theory.

Homology theory in the alternative set theory I. Algebraic preliminaries

Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris

Homomorphic correspondences of relational systems

Homomorphic images of subdirectly irreducible groupoids

Homomorphisms between $A$ -projective Abelian groups and left Kasch-rings

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Homomorphisms of a Completely Simple Semigroup onto a Group

Homomorphisms of constant stretch between Möbius groups.

Homomorphisms of Divisible Semigroups.

Homomorphisms of free contents.

Homomorphisms of group rings

Homomorphisms of nets of fixed degree, with singular points on the same line

Homomorphisms of sandwich semigroups and sandwich near-rings.

Homomorphisms of semigroups of binary relations.

Homomorphisms of semilattices of semigroups.

Currently displaying 81 – 100 of 144