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Separation theorems in the commutative algebra of -rings and applications
Communications in Algebra, 2022In this paper we state and prove ad hoc “Separation Theorems” of the so-called Smooth Commutative Algebra, the Commutative Algebra of -rings. These results are formally similar to the ones we find in (ordinary) Commutative Algebra.
J. C. Berni, H. Mariano
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Bernstein-Sato Polynomials in Commutative Algebra
Commutative Algebra, 2021This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
Josep Àlvarez Montaner +2 more
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Applications of Differential Graded Algebra Techniques in Commutative Algebra
Commutative Algebra, 2020Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
Saeed Nasseh, S. Sather-Wagstaff
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Solving Multivariate Polynomial Systems and an Invariant from Commutative Algebra
IACR Cryptology ePrint Archive, 2017The security of several post-quantum cryptosystems is based on the assumption that solving a system of multivariate (quadratic) polynomial equations $p_1=\dots=p_r=0$ over a finite field is hard.
Alessio Caminata, E. Gorla
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Quasi-S-primary ideals of commutative rings
Communications in Algebra, 2023Let R be a commutative ring with and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasi-S-primary if there exists an such that whenever and then or .
Ece Yetkin Çelikel, A. Hamed
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Deep classification of a generalization of ring filtrations in commutative algebra
International Journal of AlgebraIn this work, we propose a generalization of filtrations, which constitute an essential tool for our research in filtration theory. We present quasi-graduations of rings as an extension of our research, exploring their properties, classifications, and ...
Kouadjo Brou, Eugene Deval Beche
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Multiplicative semiprimeness of strongly semiprime non-commutative Jordan algebras
Communications in Algebra, 2022In this paper, we prove that the multiplication algebra of a nondegenerate non-commutative Jordan algebra is semiprime as a consequence of the multiplicative primeness of strongly prime non-commutative Jordan algebras, obtained previously by the two ...
A. M. Cabrera Serrano +2 more
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Commutative rings whose proper ideals are pure-semisimple
Communications in Algebra, 2023Recall that an R-module M is pure-semisimple if every module in the category is a direct sum of finitely generated (and indecomposable) modules. A theorem from commutative algebra due to Köthe, Cohen-Kaplansky and Griffith states that “a commutative ring
S. Baghdari +2 more
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Linear and multilinear algebra, 2023
Unlike quaternions and split quaternions, reduced biquaternions satisfy the multiplication commutative rule and are commonly used in image processing, fuzzy recognition, image compression, Hopfield neural networks, and digital signal processing. However,
Dong Zhang +4 more
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Unlike quaternions and split quaternions, reduced biquaternions satisfy the multiplication commutative rule and are commonly used in image processing, fuzzy recognition, image compression, Hopfield neural networks, and digital signal processing. However,
Dong Zhang +4 more
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Biderivations of a Lie algebra of Block type and applications
Communications in Algebra, 2023Let be a Lie algebra of Block type with basis and relations . In the present paper, the biderivations of are explicitly described. In particular, it is shown that any biderivation of is inner.
Jing Tang, Xiaomin Tang
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