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by Hashem Bordbar, Young Bae Jun and Seok-Zun Song

Mathematics 2020, 8(4), 567; https://doi.org/10.3390/math8040567 - 11 Apr 2020

Cited by 3 | Viewed by 2653

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras

φ : X \to Y

, we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping [...] Read more.

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras

φ : X \to Y

, we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping

c l_{Y} : I (Y) \to I (Y)

, we define a map

c l_{Y}^{\leftarrow}

I (X)

A \mapsto φ^{- 1} (φ {(A)}^{c l_{Y}}) .

We prove that, if “

c l_{Y}

” is a weak closure operation (respectively, semi-prime and meet) on

I (Y)

, then so is “

c l_{Y}^{\leftarrow}

” on

I (X)

. In addition, for mapping

c l_{X} : I (X) \to I (X)

, we define a map

c l_{X}^{\to}

I (Y)

as follows:

B \mapsto φ (φ^{- 1} {(B)}^{c l_{X}}) .

We show that, if “

c l_{X}

” is a weak closure operation (respectively, semi-prime and meet) on

I (X)

, then so is “

c l_{X}^{\to}

” on

I (Y)

. Full article

(This article belongs to the Special Issue Algebra and Discrete Mathematics 2020)

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