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...

Many patients use household cleaners to clean denture which can cause discoloration and damage soft liners. The purpose of this study was to evaluate the effect of household cleansers on the color change of two types of permanent soft liners. Methods: In this interventional study, 80 permanent silicone soft liners, including 40 heat-cured liners (Molloplast-B, Detax Gmbh & Co. ...

Many scientists have studied and improved the soft set theory, which is initiated by Molodtsov [33] and easily applied to many problems having uncertainties from social life. The main purpose of our paper, is to introduce new soft separation axioms based on the b-open soft sets which are more general than of the open soft sets. We show that, the properties of soft b-Ti-spaces (i = 1,2) are soft...

objectives: this study was designed to assess the changes of the mandible of patients who underwent orthodontic treatment with or without extraction of four premolars. materials and methods: eighteen class i bimaxillary protrusion patients treated with extraction of four first premolars and retraction of anterior teeth and 18 class i non-extraction patients with a mean age of 16.38±0.4 years we...