Geodesic
Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures
Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 274-296.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce some algebraic structure associated with rings and lattices. It appeared as the result of our new approach to the fuzzy rings and $L$-fuzzy rings where $L$ is a lattice. This approach allows us to employ more convenient language of algebraic structures instead of currently accepted language of functions.
Keywords: ring, lattice, distributive lattice, fuzzy ring
Mots-clés : homomorphism. 
@article{ADM_2017_24_2_a7,
     author = {Leonid A. Kurdachenko and Igor Ya. Subbotin and Viktoriia S. Yashchuk},
     title = {Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures},
     journal = {Algebra and discrete mathematics},
     pages = {274--296},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a7/}
}
TY  - JOUR
AU  - Leonid A. Kurdachenko
AU  - Igor Ya. Subbotin
AU  - Viktoriia S. Yashchuk
TI  - Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures
JO  - Algebra and discrete mathematics
PY  - 2017
SP  - 274
EP  - 296
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a7/
LA  - en
ID  - ADM_2017_24_2_a7
ER  - 
%0 Journal Article
%A Leonid A. Kurdachenko
%A Igor Ya. Subbotin
%A Viktoriia S. Yashchuk
%T Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures
%J Algebra and discrete mathematics
%D 2017
%P 274-296
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a7/
%G en
%F ADM_2017_24_2_a7
Leonid A. Kurdachenko; Igor Ya. Subbotin; Viktoriia S. Yashchuk. Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures. Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 274-296. http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a7/

[1] Goguen J. A., “$L$-Fuzzy Sets”, Journal of Math. Analysis and Applications, 18 (1967), 145–174 | DOI | MR | Zbl

[2] Kurdachenko L. A., Grin K. O., Turbay N. A., “On normalizers in fuzzy groups”, Algebra and Discrete Mathematics, 15 (2013), 23–36 | MR | Zbl

[3] Kurdachenko L. A., Otal J., Subbotin I. Ya., “On permutable fuzzy subgroups”, Serdica Mathematical Journal, 39 (2013), 83–102 | MR | Zbl

[4] Kurdachenko L. A., Yashchuk V. S., Subbotin I. Ya., “Lattice groups”, Algebra Discrete Math., 20 (2015), 83–102 | MR

[5] Liu Wang-Jin, “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy Sets and Systems, 8 (1982), 133–139 | DOI | MR | Zbl

[6] Liu Wang-Jin, “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy Sets and Systems, 11 (1983), 31–41 | DOI | MR | Zbl

[7] Malik D. S., Mordeson J. N., Fuzzy Commutative algebra, World Scientific, 1998 | MR | Zbl

[8] Mordeson J. N., Cheng S. C., Elements of $L$-algebras, Creighton Univ., 1994

[9] Mordeson J. N., Nair P. S., Fuzzy Mathematics, Springer, 2001

[10] Mordeson J. N., Bhutani K. R., Rosenfeld A., Fuzzy Group Theory, Springer, 2005 | Zbl

[11] Mukherjee T. K. and Sen M. K., “On fuzzy ideals of a ring”, Fuzzy Sets and Systems, 21 (1987), 99–104 | DOI | MR | Zbl

[12] Zadeh L. A., “Fuzzy sets”, Information Control, 8 (1965), 338–353 | DOI | MR | Zbl