Title of article :
On the essential CP-spaces
Author/Authors :
Majidipour, Saham Department of Mathematics - Faculty of Mathematical Sciences and Computer - Shahid Chamran University of Ahvaz, Ahvaz, Iran , Mohamadian, Rostam Department of Mathematics - Faculty of Mathematical Sciences and Computer - Shahid Chamran University of Ahvaz, Ahvaz, Iran , Namdari, Mehrdad Department of Mathematics - Faculty of Mathematical Sciences and Computer - Shahid Chamran University of Ahvaz, Ahvaz, Iran , Soltanpour, Somayeh Department of Science - Ahvaz Faculty of Petroleum - Petroleum University of Technology, Ahvaz, Iran
Abstract :
Let be the functionally countable subalgebra of . Essential -spaces are introduced and investigated algebraically and topologically. It is shown that if is a proper essential -space, then is compact if and only if is a , where is the only non -point of and is the space of minimal prime ideals of which are not maximal. Quasi -spaces, -basically disconnect spaces, almost -spaces and almost essential -spaces are introduced and studied via essential -spaces. Finally, as a -ring where is an essential -space is investigated.
Keywords :
Almost CP-point , c-basically disconnected , Essential almost CP-point , Essential CP-space , fc-space , Quasi fc-space , Space of minimal prime ideals , Von Neumann local regular ring
Journal title :
Journal of Algebraic Structures and Their Applications
