Subjects: Mathematics >> Algebra and Number Theory submitted time 2024-02-23
Abstract： This article is based on the completion of topological Abel groups, introducts topological $k$-algebras and their completions, and provides an algebraic explanation of the completion by projective limits.
Peer Review Status:
Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2023-12-11
Abstract： Let be a k-algebra defined over a field k. This paper consider the two questions: If the tensor M⊗N on A is zero, under what situation is either M = 0 or N = 0? If the element, say m⊗n , in M⊗N is zero, under what situation is either m=0 or n = 0?
Subjects: Mathematics >> Algebra and Number Theory Subjects: Mathematics >> Discrete Mathematics and Combinatorics submitted time 2023-12-04
Abstract： Let $A_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero and $X_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero. In this paper, we consider the k-tensor $A_n otimes X_n$ and the classification of the indecomposable modules over $A_n otimes X_n$. Moreover, we provide a counting formula to compute the number of isoclasses of indecomposable $A_n otimes X_n$ -modules.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2023-08-07
Abstract： It is showed that for gentle algebra, the simple module and projective module can be characterized by matrix model, and a matrix representation of projective resolution of simple module is provided. Thus the global dimension of a gentle algebra can be characterized by a
special submatrix sequence induced by its matrix model. Furthermore, by showing that above special submatrix sequences correspond to maximal non-trivial forbidden paths on the quiver of gentle algebra, the global dimension of gentle algebra equals the length of the maximal nontrivial forbidden path is obtained.
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-12-07
Abstract：
In this paper, we briefly review the characteristics of the fifth-generated method and the research results of the tone calculation, derive and prove the fractional formula of the ascending fifth’s tone series and the descending fifth’s tone series using fifth-generated method, and prove the simple formula of the fifth-generated method by combining two fractional formula of the ascending fifth’s tone series and the descending fifth’s tone series. These formulas can be used to directly calculate the pitch at any position in these series, without chain computing the middle pitch from the initial pitch. According to the simple calculation formula, the ascending and descending fifth’s tone series can be combined into a fifth’s tone series whose independent variable is an integer number. In this paper, a simple formula is used to calculate the interval between each tone and the initial tone in the fifth’s series. Based on the theory of uniform distribution, it is concluded that the infinite tone the series are Uniform Distribution within the octave. According to the three-gap theory, the number of intervals and the number of their occurrences in the pentatonic scale, the heptonic scale, the twelve-tone scale, the 60-tone of King Fang and the 360-tone of Qian Lezhi are analyzed and illustrated.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-08-07
Abstract： Cellular algebra is an algebraic structure received considerable attention in recent years, and graded algebra plays an important role in the theory of representation. Based on Wang Tao's research on precellular algebra, the definition of graded precellular algebra is given, and the representation theory of graded precellular algebra is discussed. Finally, the graded pre-cellularity of the regular semigroup algebra is studied.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2022-08-07
Abstract： Cellular algebra is an algebraic structure received considerable attention in recent years, and regular semigroup is an important semigroup, which is one of the main research fields of semigroup algebra theory. Based on the standardly based algebra proposed by Du and Rui, which is a kind of generalized cellular algebra, and the generalized cellularity of regular semigroup algebra is studied.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2016-05-19
Abstract：For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has order predicted by the Birch and Swinnerton-Dyer conjecture.
Peer Review Status:Awaiting Review
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