Related papers: Subrings of $\mathbb{C}$ Generated by Angles

Let $E$ be a module of projective dimension one over $R=k[x_1,\ldots,x_d]$. If $E$ is presented by a matrix $\varphi$ with linear entries and the number of generators of $E$ is bounded locally up to codimension $d-1$, the Rees ring…

Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that…

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A,…

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…

Let $(R, \mathfrak m)$ be a commutative noetherian local ring and $I$ an ideal of $R$. Let $\mathcal{P}$ be the class of all $I$-generated $R$-modules $M$ (i.e. there is an epimorphism $I^{(\Lambda)} \twoheadrightarrow M$) and let…

Our approach to structural matrix rings defines them over preordered directed graphs. A grading of a structural matrix ring is called a good grading if its standard unit matrices are homogeneous. For a group $G$, a $G$ -grading set is a set…

A computable ring is a ring equipped with mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However,…

Let D be a Euclidean domain, with fraction field K. Let R(D) be the subring of K generated by the reciprocals of the nonzero elements of D. The main theorem states that if R(D) is not equal to K, then R(D) is a rank 1 discrete valuation…

Let $R$ be a ring, and consider a left $R$-module given with two (generally infinite) direct sum decompositions, $A\oplus(\bigoplus_{i\in I} C_i)=M=B\oplus(\bigoplus_{j\in J} D_j),$ such that the submodules $A$ and $B$ and the $D_j$ are…

Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ K^m let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and…

We focus our attention to the set $\gl{\coring{C}}$ of grouplike elements of a coring $\coring{C}$ over a ring $A$. We do some observations on the actions of the groups $U(A)$ and $\aut{\coring{C}}$ of units of $A$ and of automorphisms of…

An exchange ring $R$ is separative provided that for all finitely generated projective right $R$-modules $A$ and $B$, $A\oplus A\cong A\oplus B\cong B\oplus B\Longrightarrow A\cong B$. Let $R$ be a separative exchange ring in which $2$ is…

A ring $R$ is called right SSP (SIP) if the sum (intersection) of any two direct summands of $R_{R}$ is also a direct summand. Left sides can be defined similarly. The following are equivalent: (1) $R$ is right SSP. (2) $R$ is right C3 and…

In this paper we study the ring of global sections of an open subset U=D(I) in Spec A, where A is a two-dimensional noetherian ring. The main concern is to give a geometric criterion when these rings are finitely generated, in order to…

Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…

Let $RG$ be the gruop ring of the group $G$ over ring $R$ and $\mathscr{U}(RG)$ be its unit group. Finding the structure of the unit group of a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit Groups of Group…

We consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we…

We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the…

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…

Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…