• Communications of the Korean Mathematical Society
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• 제31권2호
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• pp.209-216
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• 2016

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.569-573
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• 2006

Nagata and Higman proved that any nil-algebra of finite nilindex is nilpotent of finite index. The Nagata-Higman Theorem can be formulated in terms of T-ideals. TheT-ideal generated by $a^n$ for all $a{\in}A$ is also generated by the symmetric polynomials. The symmetric polynomials play an importmant role in analyzing nil-algebra. We construct the incidence matrix with the symmetric polynomials. Using this incidence matrix, we determine the nilpotency index of nil-algebra of nil-index 3.

• Bulletin of the Korean Mathematical Society
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• 제60권3호
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• pp.747-762
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• 2023

ω-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an ω-Lie algebra. In this paper, we classify ω-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of ω-Lie algebras and the technique of Lie algebras.

• Journal of the Chungcheong Mathematical Society
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• 제31권2호
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• pp.247-254
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• 2018

In this paper, we introduce the notion of symmetric bi-multiplier of subtraction algebra and investigate some related properties. Also, we prove that if D is a symmetric bi-multiplier of X, then D is an isotone symmetric bi-multiplier of X.

• Bulletin of the Korean Mathematical Society
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• 제41권2호
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• pp.359-369
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• 2004

The purpose of this paper is to compare the radicals of a left symmetric algebra considered in 〔1〕 when the associated Lie algebra is nilpotent. In this case, we show that all the radicals considered there are equal. We also consider some other radicals and show they are also equal.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.17-30
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• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.453-459
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• 2004

A left-invariant flat Riemannian connection on a Lie group makes its Lie algebra a left symmetric algebra compatible with an inner product. The left symmetric algebra is decomposed into trivial ideal and a subalgebra of e(l). Using this result, the Lie group is embedded isomorphically into the direct product of O(l) $\times$ $R^{k}$ for some nonnegative integers l and k.

• Journal of the Chungcheong Mathematical Society
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• 제32권2호
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• pp.179-189
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• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• Honam Mathematical Journal
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• 제29권2호
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• pp.119-192
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• 2007

A very important Hopf algebra is the graded Hopf algebra Symm of symmetric functions. It can be characterized as the unique graded positive selfdual Hopf algebra with orthonormal graded distinguished basis and just one primitive element from the distinguished basis. This result is due to Andrei Zelevinsky. A noncommutative graded Hopf algebra of this type cannot exist. But there is a most important positive graded Hopf algebra with distinguished basis that is noncommutative and that is twisted selfdual, the Malvenuto-Poirier-Reutenauer Hopf algebra of permutations. Thus the question arises whether there is a corresponding uniqueness theorem for MPR. This prepreprint records initial investigations in this direction and proves that uniquenees holds up to and including the degree 4 which has rank 24.

• Communications of the Korean Mathematical Society
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• 제29권3호
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• pp.463-478
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• 2014

We find criteria for symmetrized monomials to be non-hit in the $\mathcal{A}_2$-algebra of symmetric polynomials in three variables, where $\mathcal{A}_2$ is the mod 2 Steenrod algebra.