CD Tesis

KONTRUKSI DERIVASI PADA PSEUDO BE-ALJABAR

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ABSTRACT
NESSY INDRYANTIKA. 2210247917, Construction of Derivation in
Pseudo BE-Algebra, supervised by Sri Gemawati and Kartini.
A BE-algebra is a non-empty set B with a binary operation ∗ and a constant
1, usually denoted by (B; ∗; 1), which satises the following axioms: (BE1)
a ∗ a = 1, (BE2) a ∗ 1 = 1, (BE3) 1 ∗ a = a, and (BE4) a ∗ (b ∗ c) = b ∗ (a ∗ c)
for all a; b; c ∈ B. A generalization of BE-algebra, the concept of a pseudo BE-
algebra is introduced. A pseudo BE-algebra is an algebra (E; ∗; ◦; 1) satisfying
the following axioms: (pBE1) a ∗ a = 1 and a ◦ a = 1, (pBE2) a ∗ 1 = 1
and a ◦ 1 = 1, (pBE3) 1 ∗ a = a and 1 ◦ a = a, (pBE4) a ∗ (b ◦ c) = b ◦
(a ∗ c), and (pBE5) a ∗ b = 1 ⇐⇒ a ◦ b = 1 for all a; b; c ∈ E. In a
BE-algebra (B; ∗; 1), a mapping  : B → B is called a derivation in B if it
satises (x ∗ y) = (x ∗ (y)) ∨ (d(x) ∗ y), where x ∨ y = (y ∗ x) ∗ x for all
x; y ∈ B. A mapping  : B → B is called an f-derivation in B if it satises
f (x ∗ y) = (f(x) ∗ f (y)) ∨ (f (x) ∗ f(y)), where f is an endomorphism of
E. In this thesis, the concepts of derivation and f-derivation in a BE-algebra
are applied to pseudo BE-algebra, resulting in denitions and properties. The
construction of these concepts begins by dening the operations ⊖ and ⊕, which
relate the binary operations ∗ and ◦ in pseudo BE-algebra, yielding two types
of derivations called type 1 and type 2 derivations. The obtained properties
include the existence of type 1 and type 2 derivations in pseudo BE-algebra,
simple formulas for type 1 and type 2 derivations, the relationship between the
binary operations ∗ and ◦ for these two types of derivations, the xed set of
derivations in pseudo BE-algebra, the regularity concept, simple formulas for
f-derivation of an element, the relationship between the endomorphism f and
f-derivation, as well as several properties related to the ≤ relation in pseudo
BE-algebra.
Keywords: BE-algebra, pseudo BE-algebra, derivation, f-derivation, kernel,
xed set

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

2210247917

Penerbit

Pekanbaru. : Universitas Riau – FKIP – Matematika., 2025

Deskripsi Fisik

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Bahasa

Indonesia

ISBN/ISSN

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Klasifikasi

2210247917

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MAGISTER MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

RIDHO

Versi lain/terkait

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