let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

In this paper, we study depth and Stanley of the edge ideals quotient rings ideals, associated with classes graphs obtained by strong product two graphs. We consider cases when either both are arbitrary paths or one is an path other cycle. give exact formula for values some subclasses. also sharp upper bounds in general cases.

We prove that the diametral diameter two properties are inherited by F-ideals (e.g., M-ideals). On other hand, these lifted from an M-ideal to superspace under strong geometric assumptions. also show all of stable formation corresponding Köthe–Bochner spaces $$L_p$$ -Bochner spaces). Finally, we investigate when projective tensor product Banach has some property.

In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results...

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pu...

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.

The objective of this paper is to introduce the fundamental algebro-geometric constructions over the extended tropical semi-ring. The study of tropical varieties, co-varieties and ideals over this extension eventually yields the theorem of the weak tropical Nullstellensatz and gives an algebraic interpretation of the tropical Nullstellensatz.

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z0R-ideals are introduced in R which are topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...