scholarly journals CUBIC Z-SUBALGEBRAS IN Z-ALGEBRAS

2021 ◽  
Vol 2070 (1) ◽  
pp. 012085
Author(s):  
S. Sowmiya ◽  
P. Jeyalakshmi
Keyword(s):  
Homomorphic Image ◽  
Cartesian Product ◽  
Inverse Image

Abstract In this article, the notions of Cubic Z-Subalgebras in Z-algebras is introduced and some of their properties are investigated. The Z-homomorphic image and inverse image of cubic Z-Subalgebras in Z-algebras is investigated. Also, the cartesian product of cubic Z-Subalgebras in Z-algebras is also discussed.

scholarly journals A homomorphism theorem for projective planes

1971 ◽  
Vol 4 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Plane ◽  
Homomorphic Image ◽  
Inverse Image ◽  
Projective Planes ◽  
Homomorphism Theorem ◽  
Central Collineations

We prove that a non-degenerate homomorphic image of a projective plane is determined to within isomorphism by the inverse image of any one point. An application gives conditions for the preservation of central collineations by a homomorphism.

scholarly journals Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 567 ◽  
Author(s):  
Hashem Bordbar ◽  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Homomorphic Image ◽  
Inverse Image ◽  
Closure Operation ◽  
Weak Closure ◽  
Closure Operations ◽  
Epimorphic Image

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras φ : X → Y , we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping c l Y : I ( Y ) → I ( Y ) , we define a map c l Y ← on I ( X ) by A ↦ 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 ← ” on I ( X ) . In addition, for mapping c l X : I ( X ) → I ( X ) , we define a map c l X → on I ( Y ) as follows: B ↦ 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 → ” on I ( Y ) .

Characterizations of Fuzzy Sublattices Based on Fuzzy Point

2020 ◽  
pp. 105-127
Author(s):  
Chiranjibe Jana ◽  
Faruk Karaaslan
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Inverse Image ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
The Relationship

In a lattice 𝔏, the authors used the concept of belongingness and quasi-coincidence of fuzzy point to a fuzzy set, and by this notion, (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy ideal, cartesian product of (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy complemented sublattice, and cartesian product of (∈,∈∨q)-fuzzy complemented sublattice are introduced, and their properties are briefly studied. The relationship between fuzzy sublattice and (∈,∈∨q)-fuzzy sublattice, fuzzy ideal and (∈,∈∨q)-fuzzy ideal of L are established. The authors prove that the cartesian product of two (∈,∈∨q)-fuzzy ideals of a lattice is not necessarily a fuzzy ideal of a lattice. The theory of image and inverse image of an (∈,∈∨q)-fuzzy sublattice and (∈,∈∨q)-fuzzy ideal, an (∈,∈∨q)-fuzzy complemented sublattice, and (∈,∈∨q)-fuzzy complemented ideal of 𝔏 on the basis of homomorphism of lattices are also significantly established.

scholarly journals Weak Essential Fuzzy Submodules Of Fuzzy Modules

2020 ◽  
Vol 33 (4) ◽  
pp. 65
Author(s):  
Hassan K. Marhon ◽  
Hatam Y. Khalaf
Keyword(s):  
Homomorphic Image ◽  
Inverse Image

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

scholarly journals A note on complex fuzzy subfield

2021 ◽  
Vol 21 (2) ◽  
pp. 1048
Author(s):  
Muhammad Gulzar ◽  
Fareeha Dilawar ◽  
Dilshad Alghazzawi ◽  
M. Haris Mateen
Keyword(s):  
Direct Product ◽  
Homomorphic Image ◽  
Inverse Image

In this paper, we introduce idea of complex fuzzy subfield and discuss its various algebraic aspects. We prove that every complex fuzzy subfield generate two fuzzy fields and shows that intersection of two complex fuzzy subfields is also complex fuzzy subfields. We also present the concept of level subsets of complex fuzzy subfield and shows that level subset of complex fuzzy subfield form subfield.  Furthermore, we extend this idea to define the notion of the direct product of two complex fuzzy subfields and also investigate the homomorphic image and inverse image of complex fuzzy subfield.

Atanassov’s interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras

2019 ◽  
Vol 11 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Tapan Senapati ◽  
K. P. Shum
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Inverse Image ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, the notion of interval-valued intuitionistic fuzzy (IVIF) [Formula: see text]-subalgebras of [Formula: see text]-algebras are introduced and some fundamental properties are discussed. The image and the inverse image of IVIF [Formula: see text]-subalgebras are defined and how the image and the inverse image of IVIF [Formula: see text]-subalgebras in [Formula: see text]-algebras become IVIF [Formula: see text]-subalgebras are studied. Moreover, the cartesian product of IVIF [Formula: see text]-subalgebras are given.

Dosimetry and optimization in digital radiography based on the contrast-detail resolution

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Wilson Otto Gomes Batista ◽  
Alexandre Gomes De Carvalho
Keyword(s):  
Image Quality ◽  
Inverse Image ◽  
Point Of View ◽  
Complete Analysis ◽  
Portable Devices ◽  
Evaluation Tool ◽  
Air Kerma ◽  
Direct Radiography ◽  
Definition Of ◽  
Entrance Surface Air Kerma

Contrast-detail (C-D) curves are useful in evaluating the radiographic image quality in a global way. The objective of the present study was to obtain the C-D curves and the inverse image quality figure. Both of these parameters were used as an evaluation tool for abdominal and chest imaging protocols. The C-D curves were obtained with the phantom CDRAD 2.0 in computerized radiography and the direct radiography systems (including portable devices). The protocols were 90 and 102 kV in the range of 2 to 20 mAs for the chest and 80 kV in the range of 10 to 80 mAs for the abdomen. The incident air kerma values were evaluated with a solid state sensor. The analysis of these C-D curves help to identify which technique would allow a lower value of the entrance surface air kerma, Ke, while maintaining the image quality from the point of view of C-D detectability. The results showed that the inverse image quality figure, IQFinv, varied little throughout the range of mAs, while the value of Ke varied linearly directly with the mAs values. Also, the complete analysis of the curves indicated that there was an increase in the definition of the details with increasing mAs. It can be concluded that, in the transition phase for the use of the new receptors, it is necessary to evaluate and adjust the practised protocols to ensure, at a minimum, the same levels of the image quality, taking into account the aspects of the radiation protection of the patient.

CARTESIAN PRODUCT ON FUZZY IDEALS OF A TERNARY Γ-SEMIGROUP

2020 ◽  
Vol 9 (3) ◽  
pp. 1189-1195 ◽  
Author(s):  
Y. Bhargavi ◽  
T. Eswarlal ◽  
S. Ragamayi
Keyword(s):  
Cartesian Product

scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

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