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Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra
Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown...
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Algebra
Die elementare Algebra nimmt traditionell einen großen Teil der Unterrichtszeit in der Sekundarstufe I ein. Medien können den Umgang mit abstrakten...
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Gerstenhaber algebra of the Hochschild cohomology of an associative conformal algebra
We define a cup product on the Hochschild cohomology of an associative conformal algebra A , and show the cup product is graded commutative. We define...
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Structure of a Twisted Group Algebra for an Algebra Obtained by the Cayley–Dickson Process
Following some ideas proposed in [J. W. Bales, Missouri J. Math. Sci. , 21 , No. 2, 83–93 (2009)], we present an algorithm for computing basis elements...
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Algebra
The language of spectral theory is algebra, so we should begin with some kind of dictionary.
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Defining an Affine Partition Algebra
We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those...
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Symplectic Linear Algebra
A symplectic structure on a smooth manifold is defined by assigning a symplectic form to the tangent space at each point of the manifold, with...
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Two Relations for the Antisymmetrizer in the Hecke Algebra
We prove two relations for the antisymmetrizer in the Hecke algebra and derive certain restrictions imposed by these relations on unitary...
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Linear Algebra
There is no question that linear algebra is one of the cornerstones of scientific computing. Moreover, linear algebra provides an effective language...
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Linear Algebra
Linear algebra introduces students to abstract concepts associated with vectors and matrices. Some students may have already worked with matrices at...
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Time-like definition of quaternions in exterior algebra
A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three...
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Relation Graphs of the Sedenion Algebra
Let 𝕊 denote the algebra of sedenions and let Γ O (𝕊) denote its orthogonality graph. One can observe that every pair of zero divisors in 𝕊...
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What makes a Stone topological algebra Profinite
This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate...
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Resolvent Algebra in Fock-Bargmann Representation
The resolvent algebra \(\mathfrak {R}\left( X, \sigma \right) \)...
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The algebra of symmetric tensors on smooth projective varieties
In this paper, we discuss the ℂ-algebra H 0 ( X , S• T X ) for a smooth complex projective variety X . We compute it in some simple examples, and give a...
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The Formal Affine Demazure Algebra and Real Finite Reflection Groups
In this paper, we generalize the formal affine Demazure algebra of Hoffnung-MalagĂłn-LĂłpez-Savage-Zainoulline to all real finite reflection groups. We...