On generalized Beurling’s theorem and symmetry of -group algebras
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Zenobia Anusiak (1971)
Colloquium Mathematicae
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A. Schinzel, M. Zakarczemny (2006)
Colloquium Mathematicae
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The number of solutions of the congruence in the box is estimated from below in the best possible way, provided for all i,j either or or .
Shengyong Pan, Jiahui Yu (2024)
Czechoslovak Mathematical Journal
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We investigate derived equivalences between subalgebras of some -Auslander-Yoneda algebras from a class of -angles in weakly -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to -angle cases. Finally, we give an explicit example to illustrate our result.
Aldo Victorio Figallo, Gustavo Pelaitay (2015)
Mathematica Bohemica
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In 2000, Figallo and Sanza introduced -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class of tense -valued Łukasiewicz-Moisil algebras (or tense LM-algebras), namely -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...
Philip Olin (1975)
Colloquium Mathematicae
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Jan Waszkiewicz (1973)
Colloquium Mathematicae
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Attila Nagy (2020)
Commentationes Mathematicae Universitatis Carolinae
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An algebraic structure is said to be congruence permutable if its arbitrary congruences and satisfy the equation , where denotes the usual composition of binary relations. To an arbitrary -set satisfying , we assign a semigroup on the base set containing a zero element , and examine the connection between the congruence permutability of the -set and the semigroup .
Xinhong Chen, Ming Lu (2015)
Colloquium Mathematicae
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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
Grzegorz Bińczak, Joanna Kaleta, Andrzej Zembrzuski (2023)
Kybernetika
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In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra we construct set of matrices in such a way that effect algebras and are isomorphic if and only if . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most .
Elijah Eghosa Edeghagba, Branimir Šešelja, Andreja Tepavčević (2017)
Kybernetika
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The topic of the paper are -algebras, where is a complete lattice. In this research we deal with congruences and homomorphisms. An -algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an -valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce -valued congruences, corresponding quotient -algebras and -homomorphisms and we investigate connections among these notions....
Andrey Krutov, Pavle Pandžić (2024)
Archivum Mathematicum
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We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of are natural examples of such algebras.
K. Vishnu Namboothiri (2021)
Mathematica Bohemica
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Consider the linear congruence equation for , . Let denote the generalized gcd of and which is the largest with dividing and simultaneously. Let be all positive divisors of . For each , define . K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on . We generalize their result with generalized gcd restrictions on and prove that for the above linear congruence, the...
Marius Dadarlat, Wilhelm Winter (2008)
Bulletin de la Société Mathématique de France
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Suppose is a separable unital -algebra each fibre of which is isomorphic to the same strongly self-absorbing and -injective -algebra . We show that and are isomorphic as -algebras provided the compact Hausdorff space is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
Helena Rasiowa
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Contents Introduction.................................................................................................................................................. 3 § 1. System of a propositional calculus...................................................................... 4 § 2. System ..................................................................................................................... 5 § 3. -algebras.....................................................................................................................
Victor J. W. Guo, Chuanan Wei (2021)
Czechoslovak Mathematical Journal
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Let denote the th cyclotomic polynomial in . Recently, Guo, Schlosser and Zudilin proved that for any integer with , where . In this note, we give a generalization of the above -congruence to the modulus case. Meanwhile, we give a corresponding -congruence modulo for . Our proof is based on the ‘creative microscoping’ method, recently developed by Guo and Zudilin, and a summation formula.
Bjorn Poonen (2008)
Journal of the European Mathematical Society
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The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension...