the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

The discrete spectrum solutions corresponding to dually-charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes, when the magnetic charge of the nucleus exceeds the critical value.

Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of all locally compact Hausdorff spaces and all perfect maps between them. 2000 MSC: primary 18A40, 54D45; secondary 06E15, 54C10, 54E05, 06E10.

OBJECTIVE The purpose of this study was to assess the validity of self-reports of substance use among outpatients dually diagnosed with substance use disorder and either bipolar disorder or posttraumatic stress disorder. METHOD Self-reports of substance use were compared with supervised urine samples collected on the same day for 55 subjects. RESULTS Self-reports were highly valid. Only 4.7...

We present a category equivalent to that of semi-Nelson algebras. The objects in this are pairs consisting semi-Heyting algebra and one its filters. filters must contain all the dense elements satisfy an additional technical condition. also show case dually hemimorphic algebras, not necessary is