scholarly journals Abstract commutative ideal theory

1962 ◽  
Vol 12 (2) ◽  
pp. 481-498 ◽  
Author(s):  
R. P. Dilworth
Keyword(s):  
Ideal Theory ◽  
Commutative Ideal

scholarly journals Commutative ideal theory without finiteness conditions: Primal ideals

2004 ◽  
Vol 357 (7) ◽  
pp. 2771-2798 ◽  
Author(s):  
Laszlo Fuchs ◽  
William Heinzer ◽  
Bruce Olberding
Keyword(s):  
Ideal Theory ◽  
Finiteness Conditions ◽  
Commutative Ideal

Symmetric ring property on nil ideals

2018 ◽  
Vol 17 (01) ◽  
pp. 1850013
Author(s):  
Tai Keun Kwak ◽  
Yang Lee ◽  
Zhelin Piao ◽  
Young Joo Seo
Keyword(s):  
Ideal Theory ◽  
Ring Theory ◽  
Noncommutative Rings ◽  
Commutative Ideal ◽  
Ring Extensions ◽  
Lattice Of Ideals

The usual commutative ideal theory was extended to ideals in noncommutative rings by Lambek, introducing the concept of symmetric. Camillo et al. naturally extended the study of symmetric ring property to the lattice of ideals, defining the new concept of an ideal-symmetric ring. This paper focuses on the symmetric ring property on nil ideals, as a generalization of an ideal-symmetric ring. A ring [Formula: see text] will be said to be right (respectively, left) nil-ideal-symmetric if [Formula: see text] implies [Formula: see text] (respectively, [Formula: see text]) for nil ideals [Formula: see text] of [Formula: see text]. This concept generalizes both ideal-symmetric rings and weak nil-symmetric rings in which the symmetric ring property has been observed in some restricted situations. The structure of nil-ideal-symmetric rings is studied in relation to the near concepts and ring extensions which have roles in ring theory.

Note on Abstract Commutative Ideal Theory

1967 ◽  
Vol 74 (6) ◽  
pp. 706 ◽  
Author(s):  
P. J. McCarthy
Keyword(s):  
Ideal Theory ◽  
Commutative Ideal

Some results on abstract commutative ideal theory

1995 ◽  
Vol 30 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Francisco Alarcon ◽  
D. D. Anderson ◽  
C. Jayaram
Keyword(s):  
Ideal Theory ◽  
Commutative Ideal

Uni-Hesitant Fuzzy Set Approach to the Ideal Theory of BCK-Algebras

2020 ◽  
pp. 128-139
Author(s):  
G. Muhiuddin
Keyword(s):  
Level Set ◽  
Fuzzy Set ◽  
Theoretical Approach ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Commutative Ideal ◽  
Fuzzy Ideal ◽  
The Ideal

In this chapter, the author studies the uni-hesitant fuzzy set-theoretical approach to the ideals of BCK-algebras. For a hesitant fuzzy set H on S and a subset of [0,1], the set L(H;ʎ):={x∈S|xH⊆ʎ}, is called the uni-hesitant level set of H. Moreover, the author discusses the relations between uni-hesitant fuzzy commutative ideals and uni-hesitant fuzzy ideals. Further, he considered the characterizations of uni-hesitant fuzzy commutative ideals in BCK-algebras. Finally, he proved some conditions for a uni-hesitant fuzzy ideal to be a uni-hesitant fuzzy commutative ideal.

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