Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808813320231222Pseudo-irreducible elements in multiplicative latticesPseudo-irreducible elements in multiplicative lattices3763861863910.22055/jamm.2023.44360.2184FAEsmaeilRostamiDepartment of Pure Mathematics
Shahid Bahonar University of Kerman
, Kerman, IranShokoofehGhorbaniDepartment of Pure Mathematics,
Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman, IranJournal Article20230720In this paper, we define the concept of pseudo-irreducible elements in multiplicative lattices and examine its relationship with other important concepts of multiplicative lattices such as prime elements, primary elements, and maximum elements, and then with the help of this concept, we define and analyze the complete comaximal factorization in multiplicative lattices. In particular, we characterize multiplicative lattices whose every element can be written as a product of pseudo-irreducible and pairwise comaximal elements.In this paper, we define the concept of pseudo-irreducible elements in multiplicative lattices and examine its relationship with other important concepts of multiplicative lattices such as prime elements, primary elements, and maximum elements, and then with the help of this concept, we define and analyze the complete comaximal factorization in multiplicative lattices. In particular, we characterize multiplicative lattices whose every element can be written as a product of pseudo-irreducible and pairwise comaximal elements.https://jamm.scu.ac.ir/article_18639_930f4c4aeb8e53a247d80e6214c836f1.pdf