Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 875–881
This article is cited in 2 scientific papers (total in 2 papers)
Mathematical logic, algebra and number theory
On the equational Artinian algebras
P. Modabberi, M. Shahryari
Department of Pure Mathematics, University of Tabriz, Tabriz, Iran
Equational Artinian algebras were introduced in our previous work: Compactness conditions in universal algebraic geometry, Algebra and Logic, 2016, 55 (2). In this note, we define the notion of radical topology with respect to an algebra $A$ and using the well-known König lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is Noetherian. This completes the analogy between equational Noetherian and equational Artinian algebras.
algebraic structures, equations, algebraic sets, radical ideals, coordinate algebras, Zariski topology, equationally Noetherian algebras, equational Artinian algebras; radical topology.
PDF file (129 kB)
Received February 29, 2016, published October 14, 2016
P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. Èlektron. Mat. Izv., 13 (2016), 875–881
Citation in format AMSBIB
\by P.~Modabberi, M.~Shahryari
\paper On the equational Artinian algebras
\jour Sib. \`Elektron. Mat. Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Mahdiyeh Nouri, “Algebraic geometry over Heyting algebras”, Zhurn. SFU. Ser. Matem. i fiz., 13:4 (2020), 414–421
Mohammad Shahryari, Javad Tayyebi, “On the equationally Artinian groups”, Zhurn. SFU. Ser. Matem. i fiz., 13:5 (2020), 583–595
|Number of views:|