Failure of public services has been a vividly debated topic in both theory and practice of public administration. Surprisingly, only a handful of scholarly papers have empirically examined the failure management practices and provided any useful tools and techniques for managing the failure. The aim of this paper is to explore the ways in which central government administration manages the failure and how it affects the quality of their services. The study collected 568 responses from the political appointees and career civil servants across a wide range of ministries and central government agencies in the Republic of Serbia. The results indicate that the analysis of failure plays a pivotal role in the learning process and ultimately leads to the improvement of public service quality.

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.

We study topology of the independence complexes of comaximal graphs of commutative rings with identity and show that these complexes are either contractible or homotopy equivalent to sphere.

Graphs associated to algebraic objects have been widely used to encode algebraic information through pairwise relations. Many algebraic relations, however, naturally involve finite collections rather than pairs. Simplicial complexes therefore provide a higher-dimensional framework for studying algebraic objects: after encoding algebraic data as a simplicial complex, one investigates the homology and homotopy type of its geometric realization. In this paper, we present several such constructions arising from commutative rings, finite groups, and cyclotomic polynomials. These examples illustrate how simplicial complexes can retain higher-order algebraic information and how the resulting topological invariants can reflect structural properties of the underlying algebraic object.