fa منظم‌پذیری آرنز و خاصیت تجزیه‌پذیری آمار و ریاضی Mathematic علمی پژوهشی بنیادی S در این مقاله، منظم‌پذیری آرنز را بر روی عمل‌های مدولی بررسی و گزاره‌هایی  را از بکر، دلز و لائو برای حالت‌های کلی‌تر تعمیم می‌دهیم. روابطی بین مرکز توپولوژیکی عمل‌های مدولی و خاصیت تجزیه‌پذیری آن‌ها ایجاد کرده و نتایجی را در جبرهای گروه می‌گیریم. In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. We establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. In 1951 Arens shows that the second dual of Banach algebra endowed with the either Arens multiplications is a Banach algebra, see [1]. The constructions of the two Arens multiplications in lead us to definition of topological centers for with respect to both Arens multiplications. The topological centers of Banach algebras, module actions and applications of them were introduced and discussed in [3, 5, 6, 9, 15, 16, 17, 18, 19, 24, 25]. In this paper, we extend some problems from [3, 5, 6, 16, 22] to the general criterion on module actions with some applications in group algebras. Baker, Lau and Pym in [3] proved that for Banach algebra with bounded right approximate identity, is an ideal of right annihilators in and . In the following, for a Banach , we study the similar discussion on the module actions and for Banach , we show that Arens regularity , bilinear mapping , topological center , Arens regularity , bilinear mapping , topological center , 321 336 http://jsci.khu.ac.ir/browse.php?a_code=A-10-505-1&slc_lang=fa&sid=1 Kazem Haghnejad Azar کاظم حق نژاد آذر haghnejad@uma.ac.ir 1003194753284600199 1003194753284600199 Yes University of Mohghegh Ardabil دانشگاه محقق اردبیلی