Valuations and Filtrations

Quotient BCI-algebras induced by pseudo-valuations

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

Are Time Consistent Valuations Information Monotone?

Multi-period risk functionals assign a risk value to discrete-time stochastic processes. While convexity and monotonicity extend in straightforward manner from the singleperiod case, the role of information is more problematic in the multi-period situation. In this paper, we define multi-period functionals in such a way that the development of available information over time (expressed as a fil...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

α Valuations of Special Classes of Quadratic Graphs

MATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...