In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Teachers play a critical role in planning, organizing, coordinating, monitoring, and instructing, hence the topic of leadership styles receives a lot of attention. As a result, the physical education school is regarded as the most significant component of the educational process because it has the ability to weave together the teaching and educational skills, attitudes, and capacities that its students develop. Fits into their identities through her relationship with them. Teachers play a critical role in planning, organizing, coordinating, monitoring, and instructing, hence the topic of leadership styles receives a lot of attention. As a result, the physical education school is regarded the most significant aspect in the educational proces

This study evaluated the influence of administering different levels of L-arginine into eggs of 0-day-old Japanese quail embryos. On day 0 of incubation, 480 eggs (120 for each treatment group) were injected with 0% arginine (C group), 1% arginine (T1), 2% arginine (T2) or 3% arginine (T3). After hatching, 336 quail chicks (84 chicks produced from each in ovo injection treatment) were placed in an experimental quail house and allocated to four treatment groups of three replicates, with 16 quail chicks for each replicate. Traits involved in this study were hatchability rate, initial body weight (7 days of age), final body weight (42 days old), feed intake, weight gain, feed conversion ratio and blood serum glucose, protein, cholesterol, tota