相关论文: Free Cyclic Submodules and Non-Unimodular Vectors
Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply…
For a standard graded Cohen-Macaulay ring $S$, if the quotient $S/(\underline{x})$ admits non-free totally reflexive modules, where $\underline{x}$ is a system of parameters consisting of elements of degree one, then so does the ring $S$.…
In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions,…
In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector $a$ in $\mathbb{F}_{2}^{n}.$ We find the generator polynomials and the cardinality of these codes. We also study…
In Secion~1 we describe what is known of the extent to which a separable extension of unital associative rings is a Frobenius extension. A problem of this kind is suggested by asking if three algebraic axioms for finite Jones index…
Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example…
We show that if a group is not virtually cyclic and is hyperbolic relative to a family of proper subgroups, then it has a hyperbolically embedded subgroup which contains a finitely generated non-abelian free group as a finite index…
In this paper, we use free field realisations of the A-type principal, or Casimir, $W_N$ algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to…
Which groups can occur as the group of units in a ring? Such groups are called realizable. Though the realizable members of several classes of groups have been determined (e.g., cyclic, odd order, alternating, symmetric, finite simple,…
We make a detailed study of idempotent ideals that are traces of countably generated projective right modules. We associate to such ideals an ascending chain of finitely generated left ideals and, dually, a descending chain of cofinitely…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We introduce and study a nontrivial generalization of uniserial modules and rings. A module is called weakly uniserial if its submodules are comparable regarding embedding. Also, a right (resp., left) weakly uniserial ring is a ring which…
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module which is generated by $\mu$ elements but not fewer. We denote by $\operatorname{SL}_n(R)$ the group of the $n \times n$ matrices over $R$ with determinant $1$. We…
In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then…
An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…
We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…
Given the algebra $T$ of ternions (upper triangular $2\times 2$ matrices) over a commutative field $F$ we consider as set of points of a projective line over $T$ the set of all free cyclic submodules of $T^2$. This set of points can be…
In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups.
We show that the set of all (unimodular and non-unimodular) free cyclic submodules of T^2, where T is the ring of ternions over a commutative field, admits a point model in terms of a smooth algebraic variety.
The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state…