KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

An extension ofz-ideals andz◦-ideals

Ali R. ALİABAD
Sajad Nazari
Mehdi Badie
Sayfa
254–272
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This comprehensive look helps to recognizethe resemblances and differences of known concepts better.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:LetRbe a commutative with unity,Y⊆Spec(R), and $h_Y$(S) ={P∈Y:S⊆P}, foreveryS⊆R.
📊
Temel Bulgular & Veri:An idealIis said to be an $H_Y$-ideal whenever it follows from $h_Y$(a)⊆ $h_Y$(b)anda∈Ithatb∈I.
💡
Sonuç & Katkı:This comprehensive look helps to recognizethe resemblances and differences of known concepts better.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

LetRbe a commutative with unity,Y⊆Spec(R), and $h_Y$(S) ={P∈Y:S⊆P}, foreveryS⊆R. An idealIis said to be an $H_Y$-ideal whenever it follows from $h_Y$(a)⊆ $h_Y$(b)anda∈Ithatb∈I. A strong $H_Y$-ideal is defined in the same way by replacingan arbitrary finite setFinstead of the elementa. In this paper these two classes ofideals (which are based on the spectrum of the ring Rand are a generalization of thewell-known concepts semiprime ideal, z-ideal,z^circ-ideal (d-ideal), sz-ideal and s z^circ-ideal (ξ-ideal)) are studied. We show that the most important results about these concepts, "Zariskitopology", "annihilator", and etc. can be extended in such a way that the correspondingconsequences seems to be trivial and useless. This comprehensive look helps to recognizethe resemblances and differences of known concepts better.

🔖

Bu Makaleye Atıf Yap

ALİABAD, A. R., Nazari, S., Badie, M. (2022). An extension ofz-ideals andz◦-ideals. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 254–272. https://ajindex.com/articles/529693

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (1)

  1. A.R. Aliabad and M. Badie,Fixed-place ideals in commutative rings, Comment. Math.Univ. Carolin.54(1), 53–68, 2013. [2]A.R. Aliabad and M. Badie,On Bourbaki associated prime divisors of an ideal,Quaest. Math.42(4), 479-500, 2019. [3]A.R. Aliabad and R. Mohamadian,Onsz◦-ideals in polynomial rings, Comm. Algebra39(2) (2011), 701–717, 2011. [4]A.R. Aliabad, R. Mohamadian, and S. Nazari,On regular ideals in reduced rings,Filomat31(12), 3715–3726, 2017. [5]A.R. Aliabad and S. Nazari,On the spectrum of a commutative ring viaC(X), (toappear). [6]A.R. Aliabad, A. Taherifar, and N. Tayarzadeh,α-Baer rings and some related con-cepts viaC(X), Quaest. Math.39(3), 401–419, 2016. [7]G. Artico, U. Marconi, and R. Moresco,A subspace ofSpec(A)and its connexionswith the maximal ring of quotients, Rend. Sem. Mat. Univ., Padova64, 93–107, 1981. [8]M.F. Atiyah and I.G. Macdonald,Introduction to Commutative Algebra, vol. 2,Addison-Wesley Reading, 1969. [9]F. Azarpanah, O.A.S. Karamzadeh, and A.R. Aliabad,Onz◦-ideals in C(X), Fund.Math.160(1), 15-25,1999. [10]F. Azarpanah, O.A.S. Karamzadeh, and A.R. Aliabad,On ideals consisting entirelyof zero-divisors, Comm. Algebra28(2), 1061–1073, 2000. [11]T.S. Blyth,Lattices and Ordered Algebraic Structures, Springer-Verlag, London, 2005. [12]L. Gillman and M. Jerison,Rings of Continuous Functions, Van Nostrand Reinhold,New York, 1960. [13]G. Grätzer,General Lattice Theory, Birkhäuser, Basel, 1998. [14]M. Henriksen and M. Jerison,The space of minimal prime ideals of a commutativering, Trans. Amer. Math. Soc.115, 110–130, 1965. [15]C.B. Huijsmans and B. De Patger,Onz-ideals andd-ideals in Riesz spaces. I, Indag.Math. (Proceeding) A83(2), 183–195, 1980. [16]D.G. Johnson and M. Mandelker,Functions with pseudocompact support, TopologyAppl.3(4), 331–338, 1973. [17]J. Kist,Minimal prime ideals in commutative semigroups, Proc. Lond. Math. Soc.3(1), 31–50, 1963. [18]G. Mason,z-ideals and prime ideals, J. Algebra26(2), 280–297, 1973. [19]G. Mason,Prime ideals and quotient rings of reduced rings, Math. Jpn.34(6), 941–956, 1989. [20]Y. Quentel,Sur la compacité du spectre minimal d’un anneau, Bull. Soc. Math. France99, 265–272, 1971. [21]R.Y. Sharp,Steps in Commutative Algebra, Cambridge university press, London,1990. [22]S. Willard,General Topology, Addison Wesley, Reading Mass., New York, 1970.