In this paper we will introduce the notion of coprime hyperideals in multiplicative hyperrings and we will show some properties of them. Then we introduce the notion of hyperring of fractions generated by a multiplicative hyperring and then we will show some properties of them.

The aim of this paper is to investigate useful generalizations of the classical concept of a quasi-automaton without outputs or a discrete dynamical system, which are also called actions of semigroups or groups on given phase sets. The paper contains also certain applications of presented concepts and examples from various areas of mathematics.

Geographic support of decision-making processes is based on various geographic products, usually in digital form, which come from various foundations and sources. Each product can be characterized by its quality or by its utility value for the given type of task or group of tasks, for which the product is used. They also usually have different characteristics and thus can very significantly influence the resulting analytical material. The aim of the paper is to contribute to the solution of the question of how it is possible to work with diverse spatial geographic information so that the user has an idea about the resulting product. The concept of fuzzy sets is used for representation of classes, whose boundaries are not clearly (not sharply) set, namely, the fuzzy approach in overlaying operations realized in ESRI ArcGIS environment. The paper is based on a research project which is being solved at the Faculty of Military Technologies of the University of Defence. The research deals with the influence of geographic and climatic factors on the activity of armed forces and the Integrated Rescue System.

Quality education is an indispensable prerequisite for all kinds of human activities. No area of human activity if it has to function properly can exist without sophisticated education that determines the quality of workers in the given area. Training of public administration officials is a very important step to ensure conditions for adequate response in case of disasters and other emergencies. Conditions for successful solutions can be created by acquiring professional knowledge and skills, having mastered technical and technological readiness to manage critical crisis situations and creating and updating legislation interlinked with harmonizing mutual cooperation with EU countries. This article aims to highlight the inconsistence in educating "target groups" in the field of crisis management which is becoming a systematic problem in the educational system of the Czech Republic. According to § 39 of the Act no. 111/1998 Coll., on universities and on the change and amendments to other Acts, the military colleges and universities prepare specialists, particularly for armed forces. However, students, not being soldiers in active duty, can study there as well. Police colleges prepare experts especially for security forces. However, there can also study those who are not members of the security forces. Moreover, the paper analyses the possibility to prepare "a common minimum", which could be reflected in curricula of universities and colleges preparing students in the field of crisis management. The results of the analysis will be the base for the proposal, which would greatly help to resolve the situation.

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A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.

The paper is devoted to the crisis management field in the emergency medical services (EMS) in case of emergency with mass health disabilities, and education of crisis management staff.Acts related to EMS in the Czech Republic do not specify a particular professional profile and education targeted at emergency preparedness, crisis management on the list of medical professional staff. This fact is reflected in the personal equipment of EMS emergency preparedness workplaces in each region of the Czech Republic. In practice, the crisis management system is often faced with a lack of inadequately professionally trained and experienced staff. The paper suggests possible approaches to enhance the education effectiveness in the field of crisis management in pre-hospital emergency care.