Abstract:Neutrosophic N -structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.

Extending the notion of dimension of a hyperring, we introduce the concept of height of a prime hyperideal of a hyperring, similarly as in ring theory, and we present some basic properties and relations with the dimension notion. In the second part of the article we illustrate some results concerning the height of prime hyperideals in Noetherian/Artinian hyperrings. 2010 Mathematics Subject Classification. Primary 20N20 Keywords. Hyperring, prime/maximal hyperideal, Noetherian/Artinian hyperring, dimension of a hyperring, height of a prime hyperideal

Abstract:The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A, B), which consists of neutrosophic quadruple BCK/BCI-numbers with a condition, is established. Conditions for the set NQ(A, B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A, B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. An example to show that the set {0} is not a positive implicative ideal in a neutrosophic quadruple BCK-algebra is provided, and conditions for the set {0} to be a positive implicative ideal in a neutrosophic quadruple BCK-algebra are then discussed.Keywords: neutrosophic quadruple BCK/BCI-number; neutrosophic quadruple BCK/BCI-algebra; neutrosophic quadruple subalgebra; (positive implicative) neutrosophic quadruple ideal MSC: 06F35; 03G25; 08A72

In this paper, we initiate the study of the notion of support of a hypermodule over a Krasner hyperring, providing several connections with the annihilator of such hypermodules. We concentrate on the similarities/differences between these concepts and the analogous ones from classical algebra (module theory). After defining and characterizing the support of a hypermodule (and in particular of a finitely generated hypermodule), by using the notion of length of a hypermodule, we determine the support of a quotient hypermodule containing only one maximal hyperideal.

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