Minimal prime ideals of reduced rings

作者：Lee Tsiu Kwen^*; Lin Jheng Huei

来源：Communications in Algebra, 2018, 46(8): 3436-3441.

DOI：10.1080/00927872.2017.1412454

• Complete Boolean algebra
• extended centroid
• Martindale symmetric ring of quotients
• minimal prime ideal
• reduced ring
• skew derivation

Let R be a reduced ring with Q its Martindale symmetric ring of quotients, and let B be the complete Boolean algebra of all idempotents in C, where C is the extended centroid of R. It is proved that every minimal prime ideal of R must be of the form mQR for some maximal ideal m of B but the converse is in general not true. In addition, if R is centrally closed or has only finitely many minimal prime ideals, then the converse also holds. By applying the explicit expression, many properties of minimal prime ideals of reduced rings are realized more easily.

• 出版日期2018