A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

Magdalena Jankowska

Contact

Lukasz Matysiak

Contact

Kazimierz Wielki University in Bydgoszcz

A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

Article Fingerprint

ReserarchID

P91MC

A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications Banner

AI TAKEAWAY

Connecting with the Eternal Ground

Abstract

This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper contains the results of the relationship between the theory of polynomial composites, the Galois theory and the theory of nilpotents. The third part of this paper shows us some cryptosystems. We find generalizations of known ciphers taking into account the infinite alphabet and using simple algebraic methods. We also find two cryptosystems in which the structure of Dedekind rings resides, namely certain elements are equivalent to fractional ideals. Finally, we find the use of polynomial composites and monoid domains in cryptology.

References

16 Cites in Article

Reference Format

D Anderson,David Anderson,Muhammad Zafrullah (1990). Factorization in integral domains.
D Anderson,D Anderson,M Zafrullah (1991). Rings between D[X] and K[X].
David Anderson,Alain Ryckaert (1988). The class group of D + M.
J Brewer,E Rutter (1976). $D+M$ constructions with general overrings..
D Costa,J Mott,M Zafrullah (1978). The construction D + XDS[X].
Paul Eakin (1968). The converse to a well known theorem on Noetherian rings.
Marco Fontana,Salah Kabbaj (1990). On the krull and valuative dimension of D + XDs[X] domains.
Hwankoo Kim (2001). FACTORIZATION IN MONOID DOMAINS.
Andy Magid (2014). The Separable Galois Theory of Commutative Rings.
Ł Matysiak (2020). On properties of composites and monoid domains.
Ł Matysiak (2021). Generalized RSA cipher and Diffe-Hellman protocol.
Ł Matysiak (2021). On some properties of polynomial composites.
Ł Matysiak (2021). Polynomial composites and certain types of fields extensions.
Magdalena Jankowska,L Ukasz Matysiak (2021). A structure of Dedekind in the cryptosystem.
T Shah,W Khan (2010). On Factorization properties of monoid S and monoid domain D[S.
M Zafrullah (1988). The D + XDS[X] construction from GCD-domains.

Download References

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Magdalena Jankowska. 2021. \u201cA Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F3).

More Citation Formats

Select Citation Style:

Download Citation

GJSFR Volume 21 Issue F3

Explore Journals Explore Volume Read This Issue

Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

Not Found

Classification

GJSFR-F Classification MSC 2010: 08A40

Submission ReceivedMay 12, 2021
Peer Review Double Blind
Handling Editor
Accepted June 3, 2021
Published June 15, 2021

Version of record

v1.2

Issue date

July 2, 2021

Language

Experiance in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

View in VR

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

View in 3D

Article Matrices

Total Views: 2150

Total Downloads: 1022

2026 Trends

Our website is actively being updated, and changes may occur frequently. Please clear your browser cache if needed. For feedback or error reporting, please email [email protected]