Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

If T is a numerical semigroup with maximal ideal N , define associated semigroups B(T ) := (N −N) and L(T ) = ∪{(hN −hN) : h ≥ 1}. If S is a numerical semigroup, define strictly increasing finite sequences {Bi(S) : 0 ≤ i ≤ β(S)} and {Li(S) : 0 ≤ i ≤ λ(S)} of semigroups by B0(S) := S =: L0(S), Bβ(S)(S) := N =: Lλ(S)(S), Bi+1(S) := B(Bi(S)) for 0 < i < β(S), Li+1(S) := L(Li(S)) for 0 < i < λ(S). ...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

Intrinsic magnetic topological insulators (MTIs) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ and $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ are expected to realize the high-temperature quantum anomalous Hall effect dissipationless electrical transport. However, there is still a lack of ideal MTI candidates with ordering ferromagnetic (FM) grou...

Intrinsic magnetic topological insulators (MTIs) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ and $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ are expected to realize the high-temperature quantum anomalous Hall effect dissipationless electrical transport. However, there is still a lack of ideal MTI candidates with ordering ferromagnetic (FM) grou...

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...

An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain’s characterization requires the polynomial space to be ‘connected to 1’, a condition that is implied by ...