About the Normal Projectivity and Injectivity of Krasner Hypermodules

• Main Authors: Hashem Bordbar, Irina Cristea
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Axioms
• Subjects: R-hypermodule; simple hypermodule; exact chain; (normal) projective hypermodule; (normal) injective hypermodule
• Online Access: https://www.mdpi.com/2075-1680/10/2/83

Inspired by the concepts of projective and injective modules in classical algebraic structure theory, in this paper we initiate the study of the chains of hypermodules over a Krasner hyperring <i>R</i>, endowing first the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>o</mi><msubsup><mi>m</mi><mi>R</mi><mi>n</mi></msubsup><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of all normal homomorphisms between two <i>R</i>-hypermodules <i>M</i> and <i>N</i> with a structure of <i>R</i>-hypermodule. Then, our study focuses on the concepts of normal injectivity and projectivity of hypermodules over a Krasner hyperring <i>R</i>, characterizing them by the mean of chains of <i>R</i>-hypermodules.