The idea of Boolean ring has been generalized in a variety of ways by several Mathematicians. Von-Neumann regular rings, p-rings, pk−rings, Boolean–like rings , Associative rings and P1 & P2−rings are a few interesting ring theoretic generalizations of Boolean rings. Boolean-like rings developed by A.L. Foster [3] preserve and confirm to the formal properties of the Boolean ring. V. Swaminathan [4] studied the structure of Boolean-like rings and established new results regarding Boolean-like rings besides extending many of the results true for Boolean rings to Boolean-like rings. The concept of Boolean- like algebra is introduced. It is proved that a Boolean-like algebra is a Boolean algebra if and only if aΛa = a for all a. Some results pertaining to the mutual implications of Boolean-like algebra and Boolean-like ring are presented in this paper. As in the case of Boolean algebra and Boolean ring, it is proved that the Boolean-like algebra and Boolean-like ring are equivalent abstract structures.

1.
K.
Pushpalatha
,
One Sided Ideals in Boolean Near-Rings
,
IJETMAS
, Nov
2014
, Volume
2
, Issue
6
,
254
258
, .
2.
A.L.
Foster
,
The theory of Boolean-like rings
,
Trans.Amer.Math.Soc.
59
(
1946
),
166
187
.
3.
K.
Pushpalatha
,
Some Contributions to Boolean like Near rings
,
International Journal of ngineering & Technology
,
7
, (
3.34
), (
2018
),
670
673
.
4.
Srilekha
,
N.
,
Rajyalakshmi
,
K.
,
Syed
,
P.M.
,
Charan
kumar
, G.,
Pushpalatha
,
K.
A statistical analysis of perception of the people towards suicidal tendency
,
European Journal of Molecular and Clinical Medicine
, issue
7
, vol.
8
,
2020
.
5.
K.
Pushpalatha
, ‘
One Sided ideals in Boolean Near-rings
’ in
IJETMAS
, November
2014
, Volume
2
Issue
6
.
6.
K.
Pushpalatha
,
Y.V.
Reddy
,
Boolean like near-rings
in
Acta Ciencia Indica XL M
,
2014
, No.
1
,
45
54
.
7.
Pilz
,
G.
Near-rings (Revised edition)
North Holland pub.com
.(
1983
).
8.
Thomas W.
Hungerford
.
Algebra
,
Holt Rinehart and Winston Inc
;
Newyork
(
1974
)
9.
Hansen
,
D.J.
and
Boolean near-rings and weak commutativity
Jiang Luh J.Aust.Math.Soc.(seiriesA)
103
107
(
1989
)
10.
Pushpalatha
,
K. A.
Note on left ideals in zero-symmetric
Boolean near-Rings, IJMA-
5
(
2
),
20
23
(
2014
).
11.
T.
Nagaiah
,
L.
,
P. Narasimha
Swamy
and
T.
Srinivas
,
Sum of vague ideals of a near-ring
AIP Conference Proceedings
(
2019
)
2177
(
4
),
4
7
12.
Ch.
Vasavi
,
G.
Suresh
,
M.S.N.
Murthy
,
Fuzzy hukuhara delta differential and applications to fuzzy dynamic equations on time scales
,
Journal of Uncertain Systems
, Vol.
10
, No.
3
, pp.
163
180
,
2016
165.
This content is only available via PDF.
You do not currently have access to this content.