The concepts of (∈γ ,∈γ ∨ qδ)-fuzzy h-ideals and (∈γ ,∈γ ∨ qδ)-fuzzy hinterior ideals in hemirings are introduced. Some new characterization theorems of these kinds of fuzzy h-ideals are also given. In particular, we investigate prime and strong prime (∈γ ,∈γ ∨ qδ)-fuzzy h-ideals in hemirings. Finally, we show that the h-hemiregular and h-semisimple hemirings can be described by using these kin...

Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT subobjects, and as a result the theory seems to require us to consider all Smith ideals of all monoids simultaneously, rather then restricting to the Smith idea...

olds ( α̃, β̃ ) and interval valued fuzzy generalized bi-ideals with thresholds ( α̃, β̃ ) , which are generalization of interval valued fuzzy ideals, interval valued fuzzy interior ideals, interval valued fuzzy quasi ideals and interval valued fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. Characterizations of regular semigroups by the properti...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

Introduction This essay, "Does the Book of Proverbs Promise Too Much?" is poignantly fitting in this memorial volume to Professor Hasel, who exemplified both in his life and in his scholarship the highest Christian ideals. The untimely death of one of the finest Old Testament scholars makes the Book of Proverbs' heavenly promises seem detached from earth's reality. Evangelicals confess the Book...

a one-sided ideal of a ring has the insertion of factors property (or simply, ifp) if implies r for . we say a one-sided ideal of has the weakly ifp if for each , implies , for some non-negative integer . we give some examples of ideals which have the weakly ifp but have not the ifp. connections between ideals of which have the ifp and related ideals of some ring extensions are also shown.

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...

The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. D-radicals of ideals are introduced and investigated. In particular, the prime radi...