Related papers: Finite Extensions of $\mathbb{Z}_\mathrm{max}$
We consider the classes of quasimultiplicative, semimultiplicative and Selberg multiplicative functions as extensions of the class of multiplicative functions. We apply these concepts to Ramanujan's sum and its analogue with respect to…
We study inverse $\pi$-extensions of the semigroup $\mathbb{Z}_+$. It is shown that $\pi$-extension of the semigroup $\mathbb{Z}_+$ is inverse, iff its $\pi$-extension coincides with $\pi(\mathbb{Z}_+)$. The existence of a non-inverse…
A lattice-ordered group (an $\ell$-group) $G(\oplus, \vee, \wedge)$ can be naturally viewed as a semiring $G(\vee,\oplus)$. We give a full classification of (abelian) $\ell$-groups which are finitely generated as semirings, by first showing…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
We develop notions of valuations on a semiring, with a view toward extending the classical theory of abstract nonsingular curves and discrete valuation rings to this general algebraic setting; the novelty of our approach lies in the…
A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…
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…
It follows from a recent paper by Ding and Wang that any ring which is generalized supplemented as left module over itself is semiperfect. The purpose of this note is to show that Ding and Wang's claim is not true and that the class of…
The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.
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…
Every finite subunital of any generalized hermitian unital is itself a hermitian unital; the embedding is given by an embedding of quadratic field extensions. In particular, a generalized hermitian unital with a finite subunital is a…
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
We show that any countable model of a model complete theory has an elementary extension with a "pseudofinite-like" quasidimension that detects dividing.
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Let $D$ be a division ring with center $F$, $f(x_1,x_2,\dots, x_m)$ a non-central multilinear polynomial over $F$, and $w(x_1,x_2,\dots,x_m)$ a non-trivial word. In this paper, we investigate conditions under which there exists an element…
We show that there are uncountably many algebraic extensions of $\mathbb{Q}$ containing at most finitely many moduli of CM simple principally polarized abelian varieties of any fixed dimension $g\geqslant1$, generalizing a result of…
In this paper, we give the enumeration of z-classes in finite Coxeter groups.