AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
In this article, we investigate various algebraic properties of the ℱ-limit, where ℱ is a filter on the set of natural numbers ℕ. More precisely, we study its behavior under ideal-theoretic operations, as well as its interaction with structural properties of commutative rings and its connection to the ultraproduct construction.
In this paper, we give a sketch of the evolution of Universal Algebraic Geometry and Logical Geometry. These topics were systematically developed in the works by Plotkin and his followers starting from 1996. A similar theory was constructed by Remeslennikov, Miasniakov and others. We provide the reader with the example...
We construct a certain extension of the first Weyl algebra and show how it can be used to prove an analog of well-known theorem of I. Schur in the context of the first Weyl algebra. The method presented allows to construct a fractional power of an operator without assumption that it is monic.
The paper considers the generalization of the construction of orthogonal completion to all semiprime linear algebras (systems), its implementation in maximal systems of quotients similar to the symmetric Martindale ring of quotients for known examples of their description in terms of algebras of quotients of graded Lie...
It was conjectured that no presilting objects exist in the singularity category of a finite-dimensional algebra over a field except the zero object. In this note, we give counterexamples to this conjecture for algebras over fields of positive characteristic.
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