In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

The notion of an interval-valued (∈,∈ ∨q)-fuzzy subring(ideal,prime) in ring is introduced and their characterizations are investigated. Mathematics Subject Classification: 03E72,16D25

We show that prime Fano threefolds $Y$ of genus 8 have a multiplicative Chow–Künneth decomposition, in the sense Shen–Vial. As consequence, certain tautological subring Chow ring powers injects into cohomology.

We show that Gushel-Mukai fivefolds admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As consequence, certain tautological subring Chow ring powers these varieties injects into cohomology.

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z0R-ideals are introduced in R which are topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex u is represented by a geometric object R(u) and each edge (u, v) is represented by the intersection between R(u) and R(v), if it belongs to a dense subgraph, or by a curve connecting the boundaries ofR(u) andR(v), otherwise. We study a notion of plana...