المصدر: كتاب: The Algebraic Structure of Group Rings في منتدى : قسم الرياضيات السلام عليكم ورحمة الله وبركاته كتاب The Algebraic Structure of Group Rings Donald S. Passman 1979 Highly recommended by the Bulletin of the London Mathematical Society, this comprehensive, self-contained treatment of group rings was written by an authority on the subject. Suitable for graduate students, it was hailed by the Bulletin of the American Mathematical Society as "a majestic account… encyclopedic and lucid."1985 edition رابط التحميل (ملف djvu وليس pdf) هذا المحتوى يظهر للاعضاء المسجلين فقط: هذا المحتوى يظهر للاعضاء المسجلين فقط: بالتوفيق إن شاء الله
شكرا لاهتمامك وبارك الله فيك اخي الكريم ممكن ان تساعدني في الحصول عل هذا الكتاب An Introduction to Group Rings by: César Polcino Milies, and Sudarshan K. Sehga لانه هو الكتاب الذي يحاضر منه الاستاذ وبارك الله فيك
باااااااااااااااارك الله فيك اخي الكريم والله لا اعلم كيف اكافيك الله يوفقك وييسر لك امرك ويجازيك عني كل خير
1. Find two non-isomorphic graphs G and H that cannot be distinguished by the following game. There are two players (A and E). Each player has two colours, red and blue. In the first round A can pick G or H and colours some of the nodes red, E responds by colouring some of the nodes of the other graph red. In the second round A chooses G or H (he can change to the other graph if he wants to) and colours some of the nodes blue, E responds by colouring some of the nodes of the other graph blue. At this stage, the nodes of each graph are partitioned into four parts: those with no colour (white), those which are red but not blue, those which are blue but not red, and those coloured both red and blue. If one of these four regions is empty in one graph, but non-empty in the other then A has won (and he has succeeded in distinguishing the two graphs). Also, if there are two regions connected by an edge in one graph but not the other, then again A wins. In a subsequent round of the game, A "picks up" one of his colours, picks either graph, and colours some nodes in his chosen colour, E responds by picking the same colour, and reusing it to colour some nodes of the graph that A did not choose. If one of the four region becomes empty but the corresponding region in the other graph is non-empty, or if there are two regions connected by an edge in one graph but not the other then A wins. The game continues like this indefinitely. If A never wins then E eventually wins (but the game is infinitely long). To repeat the problem: we seek two non-isomorphic graphs G and H such that E has a winning strategy in the game above. The project might involve writing a computer program to construct suitable graphs and test them to see if they solve the problem.
