Geodesic
Extensions of Boolean rings and nearrings
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 58-67.

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

In this paper, we introduce the notions of left (right) Boolean rings and nearrings. We give examples to show that left (right) Boolean rings are not commutative in general. We obtain interrelations among these algebraic structures and get conditions under which the structures are commutative. Finally, we study the concept of derivations on left (right) Boolean rings and nearrings and obtain commutativity results.
Keywords: ring, nearring, Boolean ring, Boolean nearring. 
@article{JSFU_2019_12_1_a4,
     author = {Hamsa Nayak and Syam P. Kuncham and Babushri S. Kedukodi},
     title = {Extensions of {Boolean} rings and nearrings},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {58--67},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a4/}
}
TY  - JOUR
AU  - Hamsa Nayak
AU  - Syam P. Kuncham
AU  - Babushri S. Kedukodi
TI  - Extensions of Boolean rings and nearrings
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 58
EP  - 67
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a4/
LA  - en
ID  - JSFU_2019_12_1_a4
ER  - 
%0 Journal Article
%A Hamsa Nayak
%A Syam P. Kuncham
%A Babushri S. Kedukodi
%T Extensions of Boolean rings and nearrings
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 58-67
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a4/
%G en
%F JSFU_2019_12_1_a4
Hamsa Nayak; Syam P. Kuncham; Babushri S. Kedukodi. Extensions of Boolean rings and nearrings. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 58-67. http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a4/

[1] H.E. Bell, G. Mason, “On Derivations in Near-rings”, Proceeding of Near-rings and Near-Fields (Tubigen, 1985), North-Holland Mathematical Studies, 137, 1987, 31–35 | DOI | MR | Zbl

[2] S. Bhavanari, S.P. Kuncham, “Linearly Independent Elements in N-Groups with Finite Goldie Dimension”, Bull. Korean Math. Soc., 42 (2005), 433–441 | DOI | MR

[3] S. Bhavanari, S.P. Kuncham, Nearring, Fuzzy Ideals and Graph Theory, CRC press, UK, USA, 2013 | MR

[4] S. Bhavanari, Contributions to Near-rings, VDM Verlag Dr Mullar, Germany, 2010

[5] S. Bhavanari, S.P. Kuncham, B.S. Kedukodi, “Graph of a Nearring with respect to an Ideal”, Comm. Algebra, 38 (2010), 1957–1962 | DOI | MR

[6] S. Bhavanari, L. Godloza, M. Babu Prasad, S.P. Kuncham, “Ideals and Direct Products of Zero-square Nearrings”, Int. J. Algebra (Croatia), 4 (2010), 13–16 | MR | Zbl

[7] R. James Clay, A.L. Donald, “Boolean Near-ring”, Canad. Math. Bull., 12 (1969), 265–273 | DOI | MR

[8] B. Jagadeesha, S.P. Kuncham, B.S. Kedukodi, “Implications on a Lattice”, Fuzzy Inf. Eng., 8:4 (2016), 411–425 | DOI | MR

[9] B. Jagadeesha, B.S. Kedukodi, S.P. Kuncham, “Interval valued L-fuzzy ideals based on t-norms and t-conorms”, J Intell. Fuzzy Syst., 28:6 (2016), 2631–2641 | DOI | MR

[10] A.A.M. Kamal, K.H. Al-Shaalan, “Commutativity of Near-rings with Derivations by using Algebraic Substructures”, Indian J. Pure Appl. Math., 43:3 (2012), 211–225 | DOI | MR | Zbl

[11] B.S. Kedukodi, S.P. Kuncham, S. Bhavanari, “Equiprime, 3-prime and c-prime Fuzzy Ideals of Nearrings”, Soft. Comput., 13 (2009), 933–944 | DOI | Zbl

[12] B.S. Kedukodi, S.P. Kuncham, S. Bhavanari, “C-prime Fuzzy Ideals of Nearrings”, Soochow J. Math., 33 (2007), 891–901 | MR | Zbl

[13] B.S. Kedukodi, B. Jagadeesha, S.P. Kuncham, S. Juglal, “Different Prime Graphs of a Nearring with respect to an Ideal”, Nearrings, Nearfields and Related Topics, eds. S.P. Kuncham, B.S. Kedukodi, H. Panackal, S. Bhavanari, World Scientific Publisher, Singapore, 2017, 185–203 | MR | Zbl

[14] B.S. Kedukodi, S.P. Kuncham, S. Bhavanari, “Reference points and roughness”, Inform. Sci., 180:17 (2010), 3348–3361 | DOI | MR | Zbl

[15] B.S. Kedukodi, S.P. Kuncham, S. Bhavanari, “C-Prime fuzzy ideals of Rn[x]”, Int. J Contemp. Math. Sci., 8:3 (2013), 133–137 | MR | Zbl

[16] B.S. Kedukodi, S.P. Kuncham, B. Jagadeesha, “Interval valued L fuzzy prime ideals, triangular norms and partially ordered groups”, Soft Comput., 2017 | DOI | MR

[17] K. Koppula, B.S. Kedukodi, S.P. Kuncham, “Markov chains and rough sets”, Soft. Comput., 2018 | DOI

[18] S.P. Kuncham, Contributions to Near-ring Theory II, Doctoral Dissertation Acharya Nagarjuna University, 2000 | Zbl

[19] S.P. Kuncham, B. Jagadeesha, B.S. Kedukodi, “Interval valued L-fuzzy cosets of nearrings and isomorphism theorems”, Afrika Mat., 27:3 (2016), 393–408 | DOI | MR | Zbl

[20] S.P. Kuncham, B.S. Kedukodi, H. Panackal, S. Bhavanari, Nearrings, Nearfields and Related Topics, World Scientific, Singapore, 2017 | Zbl

[21] B. Lafuerza-Guillén, H. Panackal, Probabilistic Normed Spaces, Imperial College Press, World Scientific, UK, London, 2014 | MR | Zbl

[22] A. Molkhasi, “Strongly Algebraically Closed Lattices in l-groups and Semilattices”, Journal of Siberian Federal University. Mathematics $\$ Physics, 11:2 (2018), 258–263 | DOI | MR

[23] H. Nayak, S.P. Kuncham, B. S. Kedukodi, “$\Theta \Gamma$ N-group”, Mat. Vesnik., 70:1 (2018), 64–78 | MR

[24] G. Pilz, Near-rings and Near-fields, Handbook of Algebra, ed. M. Hazewinkel, Elsevier Science B. V., 1996 | MR

[25] H. Panackal, B. Lafuerza-Guillén, K.T. Ravindran, “Compactness and $\mathcal{D}-$ boundedness in Menger's 2-Probabilistic Normed Spaces”, FILOMAT, 30:5 (2016), 1263–1272 | DOI | MR

[26] K. Plasser, Subdirekte darstellung von ringen und fastringen mit boolschen eigenzchaften, Diplomarbeit, Univ. Linz, Austria, 1974

[27] Y.V. Reddy, “Recent developments in Boolean Nearrings”, Nearrings, Nearfields and Related Topics, eds. S. P. Kuncham, B.S. Kedukodi, H. Panackal, S. Bhavanari, World Scientific Publisher, Singapore, 2017 | MR | Zbl