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In this paper, we introduce the notion of 0-distributivity and 1-distributivity in join semilattices. We give some characterizations of 0-distributive join semilattices. We prove Stone type separation theorem for 0-distributive and 1-distributive join semilattices. 0-distributive normal and comaximal join semilattices have been introduced. We show that the class of 0-distributive normal join semilattice is proper super class of 0-distributive comaximal join semilattices. We also show that in presence of 1-distributivity class of 0-distributive normal and comaximal join semilattices are equivalent. [ABSTRACT FROM AUTHOR]

In this paper, we study concepts of convergence and ideal convergence of sequence of functions and investigate relationships between them and some properties such as linearity in 2-normed spaces. Also, we prove a decomposition theorem for ideal convergent sequences of functions in 2-normed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we identify the (0, *)-ideals of a demi-pseudocomplemented MS-algebra L as the kernel of the boolean congruences on L. In particular, we show that these ideals are precisely the kernels of the congruences # on L such that (L/v; *) is boolean, and that they form a sublattice of the lattice of ideals of L that is isomorphic to the interval [G, ι] of the congruence lattice of L where G is the Glivenko congruence and ι is the universal congruence. [ABSTRACT FROM AUTHOR]

In this paper we discuss p-algebras and some of their subclasses. A notion of DM-algebras is introduced which is an important subclass of p-algebras. We give some characterizations of subclasses of p-algebras. We also give some characterizations of p-ideals of a p-algebra. [ABSTRACT FROM AUTHOR]

A Γ-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a Γ-so-ring. In this paper we introduce the notions of partial ideal of partial Γ-semiring and ideal of Γ-so-ring and study the ideal theory of Γ-so-rings. [ABSTRACT FROM AUTHOR]

A Γ-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a Γ-so-ring. In this paper we introduce the notions of partial ideal of partial Γ-semiring and ideal of Γ-so-ring and study the ideal theory of Γ-so-rings. [ABSTRACT FROM AUTHOR]

In this paper we first consider the ideas of weak statistical and ideal convergence in a normed linear space and present a characterization. It should be noted that the characterization has earlier been proved in [4], but there are faults in the arguments. We present the correct argument partially. We also introduce the ideas of weak I and I* - divergences following [7] and make certain observations. [ABSTRACT FROM AUTHOR]

In this paper, we defined Weak ideal of a C-algebra and proved certain important properties of Weak ideals. It is proved that Weak ideals of any C-algebra form an algebraic lattice whenever the C-algebra possesses smallest element with respect to the partial order induced by *. [ABSTRACT FROM AUTHOR]

In this paper, we consider a collection of deductive systems of a distributive implication groupoid X. We use the concept of congruence relation with respect to deductive systems to construct a uniformity that induces a topology on X which makes this to a topological distributive implication groupoids. [ABSTRACT FROM AUTHOR]

In this paper, introducing the notion of prime convex subnearlattices the authors generalize the Stone's representation theorem for convex subnearlattices of a distributive medial nearlattice. They also show that a distributive medial nearlattice is relatively complemented if and only if its prime convex subnearlattices are unordered. Then they study the congruences of a distributive medial nearlattice containing a convex subnearlattice as a class. [ABSTRACT FROM AUTHOR]

In this paper we introduce several concepts which are useful in the development of the theory of Generalised lattices, including the notions of Strong ideals, Strong filters, R--Strong ideals, R--Strong filters, Homomorphisms, Strong homomorphisms and Strong congruences in Generalised lattices. We also introduce the concepts of Congruence and Modularity in Posets. [ABSTRACT FROM AUTHOR]