Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

In 1988 Kalai construct a large class of simplicial spheres, called squeezed spheres, and in 1991 presented a conjecture about generic initial ideals of Stanley–Reisner ideals of squeezed spheres. In the present paper this conjecture will be proved. In order to prove Kalai’s conjecture, based on the fact that every squeezed (d−1)-sphere is the boundary of a certain d-ball, called a squeezed d-b...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

In recent years, the combinatorial properties of monomials ideals [7, 10, 14] and binomial ideals [9, 10] have been widely studied. In particular, combinatorial interpretations of minimal free resolutions have been given in both cases. In this present work, we will generalize existing techniques to obtain two new results. The first is S[Λ]-resolutions of Λ-invariant submodules of k[Z] where Λ i...

Let X,Y be Banach spaces and consider the w′-topology (the dual weak operator topology) on the space (L(X,Y ), ‖.‖) of bounded linear operators from X into X with the uniform operator norm. L ′ (X,Y ) is the space of all T ∈ L(X,Y ) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X,Y ) such that T = w′ − limnTn. Financial support from the National Council for Science and ...

Bi ideals are the generalisation of quasi ideals. In this article, it is defined that notion bi-ideals in semirings on weak nearness approximation spaces. Afterwards, explained some concepts and definitions related to subject. Also, given definition m-bi (m,n)-quasi Thus, we examine relationship between .

We introduce the notion of interval valued intutionistic (S,T)-fuzzy left h-ideal (k-ideal) of a hemiring (semiring). We describe some characteristic properties and connections. Finally, we construct some equivalence relations induced by interval valued intutionistic (S,T)-fuzzy left h-ideals (k-ideals).