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Some Remarks on Rings

100%

Obojska L., O’Hara P.

Commentationes Mathematicae

2010

tom 50

nr 1

Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and $\sigma$-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring $(Z_{p(p−1)n} +, \cdot)$, where $(p, n) = 1$ there exist isomorphic groups $(G, +)$, $(H, \cdot)$, $G, H \subset Z_{p(p−1)n}$ of the order $(p − 1)$. Finally, we note that every ring $(Z_{pn}, +, \cdot)$ contains subfields $\text{mod}(pn)$.

Real-linear isometries between function algebras

88%

Miura T.

Open Mathematics

2011

tom 9

nr 4

778-788

Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and $T\left( f \right) = \kappa \overline {fo\phi }$ on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Open Mathematics

1 Miura T.

1 Obojska L.

1 O’Hara P.

1 2011

1 2010

Wyniki wyszukiwania

Some Remarks on Rings

Real-linear isometries between function algebras