The goal of this paper is to present some basic properties of Elattices and their connections with hyperstructure theory. 2000 Mathematics Subject Classification: Primary 06B99, Secondary 20N20.

This paper deals with the hyperstructures called Hv-modules. The main tools concerning the class of Hv-modules with the ordinary modules are the fundamental relations. The fundamental relations in Hv -modules and fuzzy Hv-submodules are studied in this paper. In particular, the product structure of fuzzy sets on Hv-modules is studied.

We focus on the study of the structure of hyperrings; in this paper, we recall the basics of crisp homomorphisms between hyperstructures, particularly, between hyperrings and, then, the notion of fuzzy homomorphism between hyperrings is established and its main properties are analysed.

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them. 2010 AMS Classification: 03B60, 20A05, 20N20, 97H40