Graded weakly 1-absorbing prime ideals

• Autores: Ünsal Tekir, Suat Koç, Rashid Abu Dawwas, Eda Yıldız
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 2, 2022, págs. 291-305
• Idioma: inglés
• DOI: 10.56754/0719-0646.2402.0291
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN En este artículo, introducimos y estudiamos ideales primos débilmente 1-absorbentes en anillos conmutativos gradados. Sea G un grupo y R un anillo conmutativo G-gradado con identidad no cero 1 ≠ 0. Un ideal gradado propio P de R se llama ideal primo gradado débilmente 1-absorbente si para cualquiera x, y, z ∈ h(R) no-unidades con 0 ≠ xyz ∈ P, entonces o bien xy ∈ P o z ∈ P. Entregamos muchas propiedades y caracterizaciones de ideales primos gradados débilmente 1-absorbentes. Más aún, investigamos ideales primos débilmente 1-absorbentes bajo homomorfismo, en anillos cociente, en anillos de fracciones, en idealización.

  • English

    ABSTRACT In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let G be a group and R be a G-graded commutative ring with a nonzero identity 1 ≠ 0. A proper graded ideal P of R is called a graded weakly 1-absorbing prime ideal if for each nonunits x, y, z ∈ h(R) with 0 ≠ xyz ∈ P, then either xy ∈ P or z ∈ P. We give many properties and characterizations of graded weakly 1-absorbing prime ideals. Moreover, we investigate weakly 1-absorbing prime ideals under homomorphism, in factor ring, in rings of fractions, in idealization.

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