Exercises in Basic Ring Theory

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Fundamentals....Pages 3-8
Ideals....Pages 9-14
Zero Divisors....Pages 15-17
Ring Homomorphisms....Pages 19-21
Characteristics....Pages 23-25
Divisibility in Integral Domains....Pages 27-30
Division Rings....Pages 31-33
Automorphisms....Pages 35-36
The Tensor Product....Pages 37-40
Artinian and Noetherian Rings....Pages 41-44
Socle and Radical....Pages 45-47
Semisimple Rings....Pages 49-51
Prime Ideals, Local Rings....Pages 53-57
Polynomial Rings....Pages 59-61
Rings of Quotients....Pages 63-65
Rings of Continuous Functions....Pages 67-72
Special Problems....Pages 73-76
Front Matter....Pages 77-77
Fundamentals....Pages 79-90
Ideals....Pages 91-100
Zero Divisors....Pages 101-105
Front Matter....Pages 77-77
Ring Homomorphisms....Pages 107-110
Characteristics....Pages 111-114
Divisibility in Integral Domains....Pages 115-119
Division Rings....Pages 121-125
Automorphims....Pages 127-131
The Tensor Product....Pages 133-137
Artinian and Noetherian Rings....Pages 139-144
Socle and Radical....Pages 145-151
Semisimple Rings....Pages 153-158
Prime Ideals, Local Rings....Pages 159-167
Polynomial Rings....Pages 169-172
Rings of Quotients....Pages 173-177
Rings of Continuous Functions....Pages 179-186
Special problems....Pages 187-194
Back Matter....Pages 195-199