Order complex of ideals in a commutative ring with identity

Czechoslovak Mathematical Journal

Zoran Z. ¹  Nela Milošević² 

[1] University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia;University of Donja Gorica, Faculty for Information Systems and Technologies, Donja Gorica bb, 81000 Podgorica, Montenegro

关键词: ideal;    commutative ring;    order complex;    homotopy type;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when it is homotopy equivalent to a sphere.

【 授权许可】

Unknown