Inner separation structures for topological spaces.
Characterizations of Lambek-Carlitz type
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
On inverse categories with split idempotents
We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.
A note on some discrete valuation rings of arithmetical functions
The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined.
The valuated ring of the arithmetical functions as a power series ring
The paper examines the ring of arithmetical functions, identifying it to the domain of formal power series over in a countable set of indeterminates. It is proven that is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that is a quasi-noetherian ring.
A note on -Fibonacci sequences and specially multiplicative arithmetic functions
A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.
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