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Order complex of ideals in a commutative ring with identity

Nela MiloševićZoran Z. Petrović — 2015

Czechoslovak Mathematical Journal

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...

Note on strongly nil clean elements in rings

Aleksandra KostićZoran Z. PetrovićZoran S. PucanovićMaja Roslavcev — 2019

Czechoslovak Mathematical Journal

Let R be an associative unital ring and let a R be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.

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