Related papers: On algebraic extensions and algebraic closures of …
Using the ramification theory of tame and Kaplansky fields, we show that maximal Kaplansky fields contain maximal immediate extensions of each of their subfields. Likewise, algebraically maximal Kaplansky fields contain maximal immediate…
Suppose that the underlying field is of characteristic different from $2, 3$. In this paper we first prove that the so-called stem deformations of a free presentations of a finite-dimensional Lie superalgebra $L$ exhaust all the maximal…
In this paper, we prove weak elimination of imaginaries for perfect bounded pseudo-algebraically closed fields equipped with finitely many independent valuations. Our approach combines an extension result for types to invariant types with…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
We describe relations between maximal subfields in a division ring and in its rational extensions. More precisely, we prove that properties such as being Galois or purely inseparable over the centre generically carry over from one to…
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\mathrm{SL}(5)\times\mathbb{R}^+$-structure. We show that the algebra…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper…
The concept of a skew root of a skew polynomial is used to introduce notions of algebraic closedness for $\sigma$-fields, that is, a field equipped with an endomorphism. It is shown that every $\sigma$-field can be embedded in algebraically…
Refining a constructive combinatorial method due to MacLane and Schilling, we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree. If the value group of the…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? In this article, we answer the…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
In this paper, we study extensions of valuations over algebraic field extensions without the use of the Axiom of Choice. We show a bijection between the extensions of a valuation and the maximal ideals of the relative integral closure of…
We prove that an expansion of an algebraically closed field by $n$ arbitrary valuation rings is NTP${}_2$, and in fact has finite burden. It fails to be NIP, however, unless the valuation rings form a chain. Moreover, the incomplete theory…
We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.