Related papers: On graded going-down domains, II
We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials.…
Explaining the predictions of neural black-box models is an important problem, especially when such models are used in applications where user trust is crucial. Estimating the influence of training examples on a learned neural model's…
We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with a topologically quasi-nilpotent twisted connection of level…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
Let $K$ be an infinite integral domain and $M_{n}(K)$ be the algebra of all $n\times n$ matrices over $K$. This paper aims for the following goals: Find a basis for the graded identities for elementary grading in $M_{n}(K)$ when the neutral…
In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension…
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. Rather than saying a module has a certain property or not, each module is…
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher…
We raise the following general question regarding a ring graded by a group: "If $P$ is a ring-theoretic property, how does one define the graded version $P_{\operatorname{gr}}$ of the property $P$ in a meaningful way?". Some properties of…
This review paper deals with dimension theory of polynomial rings over certain families of pullbacks. While the literature is plentiful, this field is still developing and many contexts are yet to be explored. I will thus restrict the scope…
We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover…
In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.
We introduce and study small covers that are pullbacks from the simplex, extending pullbacks from the linear model. Our main result gives several equivalent characterizations of this class, including torsion-freeness of odd-degree integral…
We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that…
An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first-…
We provide bounds on the size of operators obtained by algorithms for executing D-finite closure properties. For operators of small order, we give bounds on the degree and on the height (bit-size). For higher order operators, we give degree…