Primeness in Quantales

Flaulles Boone Bergamaschi; Regivan Hugo Nunes Santiago; Alexsandra Oliveira Andrade

doi:10.22481/recic.v1i1.4928

Primeness in Quantales

Authors

Flaulles Boone Bergamaschi uesb
Regivan Hugo Nunes Santiago UFRN
Alexsandra Oliveira Andrade

DOI:

https://doi.org/10.22481/recic.v1i1.4928

Keywords:

Primeness; Prime ideal; Strong; Quantales.

Abstract

In this paper we propose a new concept of primeness in quantales. It is proved that this concept coincide with classical definition in commutative quantales, but no longer valid in the noncommutative setting. Also, the notions of strong and uniform strong primeness are investigated.

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References

Yang L, Xu L. Roughness in quantales. Inf. Sci. 2013; 220: 568–579.

Navarro G, Cortadellas O, Lobillo FJ. Prime fuzzy ideals over noncommutative rings. Fuzzy Sets Syst. 2012; 199: 108–120.

Handelman D, Lawrence J. Strongly prime rings. Trans. Am. Math. Soc. 1975; 211: 209–223.

Luo Q, Wang G. Roughness and fuzziness in quantales. Inf. Sci. 2014; 271: 14–30.

Rosenthal KI. Quantales and their applications. Harlow: Longman Scientific & Technical; 1990. (Pitman Research Notes in Mathematics Series, 234)

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Published

2019-03-29

How to Cite

BERGAMASCHI, Flaulles Boone; SANTIAGO, Regivan Hugo Nunes; ANDRADE, Alexsandra Oliveira. Primeness in Quantales. Journal of Computer Science, [S. l.], v. 1, n. 1, p. p. 1–4, 2019. DOI: 10.22481/recic.v1i1.4928. Disponível em: https://periodicos2.uesb.br/recic/article/view/4928. Acesso em: 21 may. 2026.