Related papers: 1-Primitive Near-rings
In this paper we consider centralizers of single elements in Ore extensions of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as an algebra. We also show that for certain…
A recursive random number generator using prime reciprocals is described.
It is shown that any primitive integral Apollonian circle packing captures a fraction of the prime numbers. Basically the method consists in applying the circle method, considering the curvatures produced by a well-chosen family of binary…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra gl(m|1).
In this paper, we consider the problem of how to establish algebraic structures on nearness approximation spaces. Essentially, our approach is to define the nearness ring, nearness ideal and nearness ring of all weak cosets by considering…
We introduce a ring and a field, generated by a semigroup, and we investigate some of their properties.
We obtain a complete classification of minimal simple unitary $W$-algebras.
Given a $T$-rough definably amenable $T$-rough approximate subgroup $A$ of a group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ of bounded index in $\langle A\rangle$.
We say that a subring $R_0$ of a ring $R$ is semi-invariant if $R_0$ is the ring of invariants in $R$ under some set of ring endomorphisms of some ring containing $R$. We show that $R_0$ is semi-invariant if and only if there is a ring…
For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classification of all (not necessarily connected) solvable…
We define a primitive index of an integer in a sequence to be the index of the term with the integer as a primitive divisor. For the sequences $k^u+h^u$ and $k^u-h^u$, we discern a formula to find the primitive indexes of any composite…
This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. A proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for each…
We consider the problem of approaching real numbers with rational numbers with prime denominator and with a single numerator allowed for each denominator. We obtain basic results, both probabilistic and deterministic, draw connections to…
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
Recently, the degenerate Stirling numbers of the first kind were introduced. In this paper, we give some formulas for the degenerate Stirling numbers of the first kind in the terms of the complete Bell polynomials with higher-order harmonic…
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
This paper studies similarities and differences between the classes of rings over which each simple module is injective and rings over which each simple module is $\Sigma$-injective. The rings in the former class are called $V$-rings and…
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.