A duality is set up for skew field extensions. Dual extensions are constructed using lambda-closed fields. Inner, outer, central and plain extensions are introduced, and some of their properties are derived. An arbitrary extension is decomposed into four extensions of basic type. Galois theory is built up using duality and some theory of diagonal extensions: the dual extensions of Galois extensions. Implications are given for prime extensions and for extensions of a field which is of finite dimension over its center.
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In this project, it is addressed by computational modeling how extreme, stressful emotions affect mental processes, and how therapies such as various mindfulness therapies can be used to handle suc
h extreme emotions. ... [more] View project Technological advancements in the last century have opened numerous venues and great challenges. The use of machines and devices in everyday human life has assigned them a new societal role. Envisi
oning the machine to act as an educator, helper, supporter, mediator, negotiator, moderator, doctor, and a daily companion is the debate of the day. Emergence of such a techno-human society has brought many challenges to technologists and social scientists. A main question that still stands is whether such a societal setup will be stable. One of the crucial factors for such a setup to be successful is the humans’ levels of trust in machines. To make such artefacts more human-aware with respect to their trust, dynamical models of trust should be designed, verified, validated and embedded into them. These models will enable the machine to estimate human trust and adapt accordingly. In existing literature there are several computational models of trust which silently assume a rational basis of trust. This performance oriented, system-theoretic view of trust is not the true representation of human behaviour. As reported in many recent studies humans usually do not behave rationally under the influence of personal perception, feeling and biases. This notion of trust is called human-based trust in this project. Both system-theoretic and human-based trust models have their own domain of applications in the current socio-technological world. As interactions in the socio-technological world can be classified into three types, namely, human-human, human-machine and machine-machine. System-theoretic trust has a wide application for cases when two autonomous machines communicate or interact with each other. These machines do not have human aspects. Hence, the performance-oriented view of utility, past experiences and institutions enforcements can provide them enough to trust on each other or not. Different from a machine-machine view of interaction, human-based trust has an application in both human-machine and human-human interactions. Hence, understanding of human trust dynamics in these perspectives is necessary for progress and effective utilization of current socio-technological advancements. This project deals with modelling of human-based trust and validation of these models, which is an essential component for human-human and human-machine interaction posed under the challenges of the postmodern human society. ... [more] View project I studied Lifestyle Informatics, a variant of Artificial Intelligence, with a focus on psychology and neuroscience at the Vrije Universiteit of Amsterdam. For my bachelor's thesis is researched how
the brains of psychopaths differ from healthy individuals using neuroscientific literature and created a temporal-causal network to represent the decision-making process in a situation of moral judgment for psychopaths. ... [more] View project August 2015 · Journal of Pure and Applied Algebra
Protoadditive functors are designed to replace additive functors in a
non-abelian setting. Their properties are studied, in particular in
relationship with torsion theories, Galois theory, homology and factorisation
systems. It is shown how a protoadditive torsion-free reflector induces a chain
of derived torsion theories in the categories of higher extensions, similar to
the Galois structures of
... [Show full abstract] higher central extensions previously considered in
semi-abelian homological algebra. Such higher central extensions are also
studied, with respect to Birkhoff subcategories whose reflector is
protoadditive or, more generally, factors through a protoadditive reflector. In
this way we obtain simple descriptions of the non-abelian derived functors of
the reflectors via higher Hopf formulae. Various examples are considered in the
categories of groups, compact groups, internal groupoids in a semi-abelian
category, and other ones. Read more Chapter
Full-text available
February 1976
Prime extensions are extensions that have no nontrivial intermediate fields. In this chapter, it is explored what types of them are possible. It is shown that any prime extension is of one of the three types outer central, inner plain or outer plain. Moreover, for type outer central it is shown that L/K is prime iff Z(L)/Z(K) is, and for type inner plain that L/K is prime iff Z(K)/Z(L) is.
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Full-text available
February 1976
In this chapter duality relations between Galois extensions and diagonal extensions of skew fields are explored and based on duality new proofs of the main theorems of Galois theory are obtained.
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March 2002 · Journal of Algebra
For a skew field extension L/K, a number of intermediate fields can be defined on the basis of the centralizer of K in L. In this paper such intermediate fields are studied in detail. Among the results are a standard decomposition of any skew field extension of finite degree and four types of skew field extensions that are basic to such a standard decomposition. A number of persistence properties
... [Show full abstract] of these types are explored. View full-text Chapter
Full-text available
February 1976
This chapter provides an overview of some basics that are needed to set up a duality for skew field extensions. It briefly discusses notions such as centralisers, normalising or diagonal elements, crossed products and pseudolinear extensions. This chapter also includes a new and simple proof of the well-known Cartan-Brauer-Hua Theorem.
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