We introduce an endofunctor H on the category baℓ of bounded archimedean ℓ-algebras and show that there is a dual adjunction between Alg(H) algebras for Coalg(V) coalgebras Vietoris V compact Hausdorff spaces. prove Gelfand duality lifts to equivalence full reflective subcategory Algu(H) Alg(H). provide alternate view by introducing Hu consisting uniformly complete objects showing Alg(Hu) isomo...

1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...

A ring of continuous functions is a ring of the form C(X), the ring of all continuous real-valued functions on a completely regular Hausdorff space X. With each ideal / of C(X), we associate certain subalgebras of C(X), and discuss their structure spaces. We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces. Introducti...

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $$A $$ be a ring with nonzero identity $$1\ne 0.$$ A proper ideal $$P of is said to if for every nonunits $$x,y,z\in $$0\ne xyz\in P, then $$xy\in P$$ or $$z\in P. In addition give many properties characterizations ideals, we also determine rings which prime. Furthermore, investigate C(X), the continuous...

In this paper we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then it is Dedekind-finite. Second, we prove a partial converse. We also prove that all clean decompositions on submodules of continuous modules extend to the entire module.

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

Experiments were designed to investigate the influence of steady flow and pressure on endothelial function in the rabbit carotid artery. Increases and decreases in isometric force were compared in static rings and perfused (5 or 50 ml/min) segments of the same arteries in the presence and absence of endothelium. The alpha(1)-adrenoceptor agonist phenylephrine and the muscarinic agonist acetylch...