Interrelations between some types of semiring ideals

Ivanna Melnyk

Анотація


The paper is focused on further study of some types of ideals of differential semirings, not necessarily commutative, i. e. prime differential ideals, differentially prime ideals and quasi-prime ideals. Some interrelation between these types of semiring ideals is established.

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J. S. Golan, Semirings and their applications, Kluwer Academic Publishers, 1999.

U. Hebisch and H. J. Weinert, Semirings: algebraic theory and applications in computer science, World Scientific, 1998.

I. Kaplansky, Introduction to differential algebra, Graduate Texts in Mathematics, 189, Springer-Verlag, 1999.

W. F. Keigher, Prime differential ideals in differential rings, Contributions to Algebra, A Collection of Papers Dedicated to Ellis Kolchin, Academic Press, 1977, pp. 239-249.

W. F. Keigher, Quasi-prime ideals in differential rings, Houston J. Math. 4 (1978), no. 3, 379-388.

Dj. Khadjiev and F. Callalp, On a differential analog of the prime-radical and properties of the lattice of the radical differential ideals in associative differential rings, Turk. J. Math. 20 (1996), no. 4, 571-582.

S. E. Kolchin, Differential algebra and algebraic groups, Academic Press, 1973.

I. Melnyk, Differentially prime, quasi-prime and Δ-MP-modules, Bul. Acad. Stiinte Repub. Mold., Mat. 3 (58) (2008), 112-115.

I. Melnyk, On the radical of a differential semiring ideal, Visn. L'viv. Univ., Ser. Mekh.-Mat. 82 (2016), 163-173.

I. Melnyk, On quasi-prime differential semiring ideals, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Informat. 37 (2020) (2). P. 63-69. DOI: 10.24144/2616-7700.2020.2(37).75-81

I. Melnyk, On quasi-prime subsemimodules, Visn. L'viv. Univ., Ser. Mekh.-Mat. 93 (2022), 66-73. DOI: 10.30970/vmm.2022.80.066-073

I. Melnyk, On differentially prime subsemimodules, Bul. Acad. Stiinte Repub. Mold., Mat. 3 (97) (2021), 30-35.




DOI: http://dx.doi.org/10.30970/vmm.2023.95.067-072

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