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Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Paradistributive Latticoid (PDL) as a generalization of a distributive lattice is introduced and investigated its properties. A set of equivalent conditions for a PDL to become a distributive lattice are given. The notions of an ideal and a filter in a PDL are introduced and studied their properties. Subdirect representation of a PDL is obtained [ABSTRACT FROM AUTHOR]

In this paper the notions of radical, prime radical and quasi prime radical are extended to seminearrings and the results analogue to those on prime radical and quasi prime radical are presented. We also obtained the class of right duo seminearrings in various characteristic in terms of ideals. [ABSTRACT FROM AUTHOR]

Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets. [ABSTRACT FROM AUTHOR]

In this paper, we introduce β-paracompactness with respect to an ideal (I-β-paracompactness) as a weak form of β-paracompactness and I-paracompactness. We give some relations between this concept and some other types of paracompactness, and also we study some of its fundamental properties. [ABSTRACT FROM AUTHOR]

The notion of β1-paracompactness in topological spaces is introduced and studied in [1]. In this paper, we introduce and investigate the notion of β1-paracompact spaces with respect to an ideal I which is a generalization of the notion of β1-paracompact spaces. We study characterizations, subsets and subspaces of β1I-paracompact spaces. Also, we investigate the invariants of β1I-paracompact spaces by functions. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring. A mapping F: R → R (not necessarily additive) is called a multiplicative (generalized) reverse derivation if there exists a map d: R → R (not necessarily a derivation nor an additive map) such that F(xy) = F(y)x + yd(x) for all x; y 2 R. In this paper we investigate some identities involving multiplicative (generalized) reverse derivation and prove some theorems in which we characterize these mappings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the intuitionistic fuzzy Zweier I-convergent double sequence spaces 2Ƶ I(μ,ν) (M) and 2ƵI0(μ,ν) (M) defined by Orlicz function and study the fuzzy topology on the said spaces. [ABSTRACT FROM AUTHOR]

To evaluate the goodness-of-fit of a statistical model to given data, calculating a conditional p value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain, which is needed for unbiasedness of the estimation, and therefore is investigated in various settings such as incomplete tables or subtable sum constraints. In this paper, we consider the two-way change-point model for the ladder determinantal table, which is an extension of these two previous works, i.e., works on incomplete tables by Aoki and Takemura (2005, J. Stat. Comput. Simulat.) and subtable some constraints by Hara, Takemura and Yoshida (2010, J. Pure Appl. Algebra). Our main result is based on the theory of Gröbner basis for the distributive lattice. We give a numerical example for actual data. [ABSTRACT FROM AUTHOR]

A convolution is a mapping C of the set (ℱ+ of positive integers into the set P ((ℱ+) of all subsets of (ℱ+ such that, for any n ϵ (ℱ+ , each member of C(n) is a divisor of n. If D(n) is the set of all divisors of n, for any n, then D is called the Dirichlet's convolution. Corresponding to any general convolution C, we can define a binary relation ≤C on (ℱ+ by "m (≤C n if and only if m ϵ C(n)". It is well known that (ℱ+ has the structure of a distributive lattice with respect to the division order. The division ordering is precisely the partial ordering =D induced by the Dirichlet's convolution D. In this paper, we present a characterization for the prime ideals in ((ℱ+,≤D) , where D is the Dirichlet's convolution. [ABSTRACT FROM AUTHOR]

An ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed sets was introduced by Levine. In this paper, we introduce and investigate the concept of generalized closed sets with respect to an ideal. [ABSTRACT FROM AUTHOR]