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<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>ϕ</mi> </math> -<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>δ</mi> </math>-Primary Hyperideals in Krasner Hyperrings

Hao Guan,Elif Kaya,Melis Bolat,Serkan Onar,Bayram Ali Ersoy,Kostaq Hila

Mathematics
Algebra over a field
    Cite this:
Guan, H., Kaya, E., Bolat, M., Onar, S., Ersoy, B. A., & Hila, K. (2022). <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>ϕ</mi> </math> -<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>δ</mi> </math>-Primary Hyperideals in Krasner Hyperrings. Mathematical Problems in Engineering, 2022, 1. https://doi.org/10.1155/2022/1192684
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In this paper, we study commutative Krasner hyperrings with nonzero identity. <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>ϕ</mi> </math> -prime, <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mi>ϕ</mi> </math> -primary and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi>ϕ</mi> </math> - <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mi>δ</mi> </math> -primary hyperideals are introduced. The concept of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mi>δ</mi> </math> -primary hyperideals is extended to <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <mi>ϕ</mi> </math> - <math xmlns="http://www.w3.org/1998/Math/MathML" id="M9"> <mi>δ</mi> </math> -primary hyperideals. Some characterizations of hyperideals are provided to classify them. The relation between <math xmlns="http://www.w3.org/1998/Math/MathML" id="M10"> <mi>ϕ</mi> </math> - <math xmlns="http://www.w3.org/1998/Math/MathML" id="M11"> <mi>δ</mi> </math> -primary hyperideals and other hyperideals is discussed.