The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

A subalgebra $B$ of a Lie algebra $L$ is called weak c-ideal if there subideal $C$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ the largest ideal contained in $B.$ This analogous to concept weakly c-normal subgroups, which has been studied by number authors. We obtain some properties c-ideals use them give characterisations solvable supersolvable algebras. also note one-dimensional ...

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...

In the frame of fractional calculus, term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus objective this review paper present Hermite–Hadamard (H-H)-type inequalities involving a variety classes convexities pertaining integral operators. Included various are classical convex functions, m-convex r-convex (α,m)-convex (α,m)-geometric...

Lee in 1970 determined the equational subclasses m B of the class of all pseudo complemented lattices. Then many authors have worked with the lattices which are in m B , sectionally in m B and relatively in m B . In this paper we extend some of their results in terms of n-ideals. We will study those ( ) L Fn which are relatively in m B . Here we include a number of characterizations of those ( ...

A completion via Frink ideals is used to define a convex powerdomain of an arbitrary continuous lattice as a continuous lattice. The powerdomain operator is a functor in the category of continuous lattices and continuous inf-preserving maps and preserves projective limits and surjectivity of morphisms; hence one can solve domain equations in which it occurs. Analogous results hold for algebraic...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

In the present paper, we characterize all possible Hilbert functions of graded ideals in a polynomial ring whose regularity is smaller than or equal to d, where d is a positive integer. In addition, we prove the following result which is a generalization of Bigatti, Hulett and Pardue’s result: Let p ≥ 0 and d > 0 be integers. If the base field is a field of characteristic 0 and there is a grade...