Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

We explicitly calculate the normal cones of all monomial primes which define the curves of the form (tL, tL+1, . . . , tL+n), where n ≤ 4. All of these normal cones are reduced and Cohen-Macaulay, and their reduction numbers are independent of the reduction. These monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integr...

Background: Sacrococcygeal pilonidal disease (PD) is prevalent in the young adults. The cause of PD is unclear, and there are different surgical procedures for the treatment. The Pilonidal sinus disease is an unpleasant, chronic relapsing condition that is difficult to cure. There is a wide variety of surgical treatments with sub-optimal results for it. The ideal treatment for the pilonidal sin...

We construct a Banach space Z such that the lattice of closed two-sided ideals of the Banach algebra B(Z) of bounded operators on Z is as follows: {0} ⊂ K (Z) ⊂ E (Z) ⊂ ⊂ M1 M2 ⊂ ⊂ We then determine which kinds of approximate identities (bounded/left/right), if any, each of the four non-trivial closed ideals of B(Z) contains, and we show that the maximal ideal M1 is generated as a left ideal by...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

In this paper, a new analytical method based on the direct synthesis approach is proposed for the design of a multi-loop proportional-integral-derivative (PID) controller. The proposed design method is aimed to achieve a desired closed-loop response for the multiple-input, multiple-output (MIMO) processes with multiple time delays. The ideal multi-loop controller is firstly designed in terms of...

Given a closed ideal I in a C-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism α : A → M(I) and a map L : J → A with some properties, based on [3] and [9] we define a C-algebra O(A,α, L) which we call the Crossed Product by a Partial Endomorphism. In the second section we introduce the Crossed Product by a Partial Endomorphism O(X,α, L) induced by a local homeomorphism σ : ...