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1. Note on a variation of the Schröder-Bernstein problem for fields

Creator:
Cater, F. S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
field, subfield, isomorphism, transcendental extension, and algebraic extension
Language:
English
Description:
In this note we study fields $F$ with the property that the simple transcendental extension $F(u)$ of $F$ is isomorphic to some subfield of $F$ but not isomorphic to $F$. Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On commutative twisted group rings

Creator:
Mollov, Todor Zh. and Nachev, Nako A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
unit groups, isomorphism, Ulm-Kaplansky invariants, and commutative twisted group rings
Language:
English
Description:
Let $G$ be an abelian group, $R$ a commutative ring of prime characteristic $p$ with identity and $R_tG$ a commutative twisted group ring of $G$ over $R$. Suppose $p$ is a fixed prime, $G_p$ and $S(R_tG)$ are the $p$-components of $G$ and of the unit group $U(R_tG)$ of $R_tG$, respectively. Let $R^*$ be the multiplicative group of $R$ and let $f_\alpha (S)$ be the $ \alpha $-th Ulm-Kaplansky invariant of $S(R_tG)$ where $\alpha $ is any ordinal. In the paper the invariants $f_n(S)$, $ n\in \mathbb{N}\cup \lbrace 0\rbrace $, are calculated, provided $G_p=1$. Further, a commutative ring $R$ with identity of prime characteristic $p$ is said to be multiplicatively $p$-perfect if $(R^*)^p = R^*$. For these rings the invariants $f_\alpha (S)$ are calculated for any ordinal $\alpha $ and a description, up to an isomorphism, of the maximal divisible subgroup of $S(R_tG)$ is given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Some properties of orders of quaternion algebras with regard to the discrete norm

Creator:
Horníček, Jan, Kureš, Miroslav, and Macálková, Lenka
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
order in an imaginary quadratic field, order in a quaternion algebra, discretely normed ring, isomorphism, and primitive algebra
Language:
English
Description:
Quaternion algebras ( −1,b ⁄ ℚ ) are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public