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1
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On free subgroups of units in quaternion algebras

100%
Krempa J.
Colloquium Mathematicum
|
2001
|
tom 88
|
nr 1
21-27
EN
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments as simple as possible.
2
Content available remote

On finiteness conditions for subalgebras with zero multiplication

100%
Krempa J.
Colloquium Mathematicum
|
2005
|
tom 102
|
nr 1
123-135
EN
Let F be a commutative ring with unit. In this paper, for an associative F-algebra A we study some properties forced by finite length or DCC condition on F-submodules of A that are subalgebras with zero multiplication. Such conditions were considered earlier when F was either a field or the ring of rational integers. In the final section, we consider algebras with maximal commutative subalgebras of finite length as F-modules and obtain some results parallel to those known for ACC condition or finite generation.
3
Content available remote

On free subgroups of units in quaternion algebras II

100%
Krempa J.
Colloquium Mathematicum
|
2003
|
tom 97
|
nr 1
29-32
EN
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
4
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Preface, Contents, List of Participants

45%
Balcerzak S., Józefiak T., Krempa J., Simson D., Vogel W.
Banach Center Publications
|
1990
|
tom 26
|
nr 2
1-10
5
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Preface, Contents, List of Participants

45%
Balcerzyk S., Józefiak T., Krempa J., Simson D., Vogel W.
Banach Center Publications
|
1990
|
tom 26
|
nr 1
1-10
6
Content available remote

Logical connections between some open problems concerning nil rings

38%
Krempa J.
Fundamenta Mathematicae
|
1972
|
tom 76
|
nr 2
121-130
7
Content available remote

Rings in which ideals are annihilators

32%
Jaegermann M., Krempa J.
Fundamenta Mathematicae
|
1972
|
tom 76
|
nr 2
95-707
8
Content available remote

Radicals of semi-group rings

26%
Krempa J.
Fundamenta Mathematicae
|
1974
|
tom 85
|
nr 1
57-71
9
Content available remote

Homomorphisms of group rings

26%
Krempa J.
Banach Center Publications
|
1982
|
tom 9
|
nr 1
233-255
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