Geodesic
Order complex of ideals in a commutative ring with identity
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 947-952
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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.
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.
DOI : 10.1007/s10587-015-0219-9
Classification : 05E40, 06A07, 13A99, 55P15
Keywords: ideal; commutative ring; order complex; homotopy type 
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Milošević, Nela; Petrović, Zoran Z. Order complex of ideals in a commutative ring with identity. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 947-952. doi: 10.1007/s10587-015-0219-9

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