Summary . In this paper, we discuss the properties that hold in finite dimensional vector spaces and related spaces. Mizar language [1], [2], variables are strictly typed, their type conversion requires a complicated process. Our purpose is to formalize some of preserved transformations, contain complexity transformations into paper. Specifically, show such as algebraic structure, subsets, sequ...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

fluency in a second language (l2) involves a quintessentially cognitive processing system that operates quickly and effectively. the perceived importance of researching fluency through a psycholinguistic lens has motivated the related l2 research to resort to current cognitive speaking-specific models. this study, drawing on levelt’s (1999a) psycholinguistic model, probed the deficiency sources...