• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.1-7
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• 2016

Some properties of filters are studied with respect to a congru-ence of BE-algebras. The notion of θ-filters is introduced and these classes of filters are then characterized in terms of congruence classes. A bijection is obtained between the set of all θ-filters of a BE-algebra and the set of all filters of the respective BE-algebra of congruences classes.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.165-178
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• 2022

In this paper, Sheffer stroke BL-algebra and its properties are investigated. It is shown that a Cartesian product of two Sheffer stroke BL-algebras is a Sheffer stroke BL-algebra. After describing a filter of Sheffer stroke BL-algebra, a congruence relation on a Sheffer stroke BL-algebra is defined via its filter, and quotient of a Sheffer stroke BL-algebra is constructed via a congruence relation. Also, it is defined a homomorphism between Sheffer stroke BL-algebras and is presented its properties. Thus, it is stated that the class of Sheffer stroke BL-algebras forms a variety.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.997-1033
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• 2024

We use Borcherds products to give a new construction of the weight 3 paramodular nonlift eigenform f_N for levels N = 61, 73, 79. We classify the congruences of f_N to Gritsenko lifts. We provide techniques that compute eigenvalues to support future modularity applications. Our method does not compute Hecke eigenvalues from Fourier coefficients but instead uses elliptic modular forms, specifically the restrictions of Gritsenko lifts and their images under the slash operator to modular curves.