Valuations on a commutative ring

A Note on a graph associated to a commutative ring

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...

On perfectness of dot product graph of a commutative ring

Let $A$ be a commutative ring with nonzero identity, and $1leq n

Study on the new graph constructed by a commutative ring

Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation b...

Commutative Pseudo valuations on BCK-Algebras

D. Buşneag 1 defined pseudo valuation on a Hilbert algebra and proved that every pseudo valuation induces a pseudometric on a Hilbert algebra. Also, D. Buşneag 2 provided several theorems on extensions of pseudo valuations. C. Buşneag 3 introduced the notions of pseudo valuations valuations on residuated lattices, and proved some theorems of extension for these using the model of Hilbert algebr...

Approximation theorems for valuations on commutative rings