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Unions of subquasigroups

Tomáš Kepka, Pavel Příhoda, Jan Šťovíček (2004)

Acta Universitatis Carolinae. Mathematica et Physica

Unique a -closure for some -groups of rational valued functions

Anthony W. Hager, Chawne M. Kimber, Warren W. McGovern (2005)

Czechoslovak Mathematical Journal

Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct a -closures. Here, we find a reasonably large class with unique and perfectly describable a -closure, the class of archimedean -groups with weak unit which are “ -convex”. ( is the group of rationals.) Any C ( X , ) is -convex and its unique a -closure is the Alexandroff algebra of functions on X defined from the clopen sets; this is sometimes C ( X ) .

Unique prime factorization in a partial semigroup of matrix-polynomials

Michael Kaltenbäck, Harald Woracek (2006)

Discussiones Mathematicae - General Algebra and Applications

We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.

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