Necklace rings and logarithmic functions

Necklace Rings and Logarithmic Functions

In this paper we develop the theory of a necklace ring and the theory of a logarithmic function (associated with graded Lie algebras and Lie superalgebras). Related to a necklace ring, we show that its construction is functorial. On a logarithmic function we generalize the results in Bryant (J. Algebra. 253 (2002); no.1, 167-188) to the cases of graded Lie (super)algebras with a group action by...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Unambiguous Functions in Logarithmic Space

We investigate different variants of unambiguity in the context of computing multi-valued functions. We propose a modification to the standard computation models of Turing machines and configuration graphs, which allows for unambiguity-preserving composition. We define a notion of reductions (based on function composition), which allows nondeterminism but controls its level of ambiguity. In lig...

Plurisubharmonic functions with logarithmic singularities

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Rings of Quotients of Rings of Functions