A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .
In Baghdad city, Iraq, the traffic volumes have rapidly grown during the last 15 years. Road networks need to reevaluate and decide if they are operating properly or not regarding the increase in the number of vehicles. Al-Jadriyah intersection (a four-leg signalized intersection) and Kamal Junblat Square (a multi-lane roundabout), which are two important intersections in Baghdad city with high traffic volumes, were selected to be reevaluated by the SIDRA package in this research. Traffic volume and vehicle movement data were abstracted from videotapes by the Smart Traffic Analyzer (STA) Software. The performance measures include delay and LOS. The analysis results by SIDRA Intersection 8.0.1 show that the performance of the roundab
... Show MoreLet R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of
... Show MorePermanent deformation, fatigue and thermal cracking are the three typical distresses of flexible pavement. Using hydrated lime (HL) into the conventional limestone mineral additive has been widely practiced, including in Europe, to improve the mechanical properties of hot mix asphalt (HMA) concrete and as the result the durability of the constructed pavement. Large number of experimental studies have been reported to find the optimum addition of HL for the improvement on HMA concrete mechanical properties, moisture susceptibility and fatigue resistance. Pavement in service is under complex thermomechanical stress-strain conditions due to coupled atmospheric and surrounding environment temperature variation and the traffic loading. To predic
... Show MoreA non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.
Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.