Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

Remark (Ideals versus subrings): It is worthwhile to compare these two notions; they are related, but with subtle and important differences. Both an ideal I and a subring S of a ring R are subsets of R which are subgroups under addition and are stable under multiplication. However, each has an additional property: for an ideal it is the absorption property (IR2). For instance, the integers Z ar...

The Tip-Edge bracket features the first and only archwire slot that offers variable control levels. It’s .022" archwire slot can increase in size to .028" relative to the archwire during retraction yet close back down to .022" to facilitate final finishing. Variable control eliminates the excessive anchorage strain and bite deepening that occurs during retraction with conventional edgewise appl...

We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals ...

Given an ideal I on ω let a(I) (ā(I)) be minimum of the cardinalities of in nite (uncountable) maximal I-almost disjoint subsets of [ω]. We show that a(Ih) > ω if Ih is a summable ideal; but a(Z~ μ) = ω for any tall density ideal Z~ μ including the density zero ideal Z. On the other hand, you have b ≤ ā(I) for any analytic P -ideal I, and ā(Z~ μ) ≤ a for each density ideal Z~ μ. For each ideal ...

We define a Riesz type interpolation property for the Cuntz semigroup of a C∗-algebra and prove it is satisfied by the Cuntz semigroup of every C∗-algebra with the ideal property. Related to this, we obtain two characterizations of the ideal property in terms of the Cuntz semigroup of the C∗-algebra. Some additional characterizations are proved in the special case of the stable, purely infinite...

let $f: arightarrow b$ be a ring homomorphism and let $j$ be an ideal of $b$. in this paper, we investigate the transfer of the property of coherence to the amalgamation $abowtie^{f}j$. we provide necessary and sufficient conditions for $abowtie^{f}j$ to be a coherent ring.

in this paper, we first present a new important property for bouligand tangent cone (contingent cone) of a star-shaped set. we then establish optimality conditions for pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.