Journal of Algebra and Related Topics
Volume:6 Issue: 1, Summer 2018

In this paper, N
-fuzzy UP-subalgebras (resp., N-fuzzy UP-filters, N-fuzzy UP-ideals and N-fuzzy strongly UP-ideals) of UP-algebras are introduced and proved its generalizations and characteristic N-fuzzy sets of UP-subalgebras (resp., UP-filters, UP-ideals and strongly UP-ideals).
Further, we discuss the relations between N-fuzzy UP-subalgebras (resp., N-fuzzy UP-filters, N-fuzzy UP-ideals and N
-fuzzy strongly UP-ideals) and its level subset

Let R
be a commutative ring and H a nonempty proper subset of R.
In this paper, the extended total graph, denoted by ETH(R) is presented, where H is a
multiplicative-prime subset of R. It is the graph with all elements of R as vertices, and for distinct p,q∈R, the vertices p and q are adjacent if and only if rp+sq∈H for some r,s∈R∖H. We also study the two (induced) subgraphs ETH(H) and ETH(R∖H), with vertices H and R∖H, respectively. Among other things, the diameter and the girth of ETH(R)
are also studied

Let R
be a commutative ring with nonzero identity. Let Γ(R) denotes the maximal graph corresponding to the non-unit elements of R, that is, Γ(R)
is a graph with vertices the non-unit elements of R, where two distinct
vertices a and b are adjacent if and only if there is a maximal ideal of R
containing both. In this paper, we investigate that for a given positive integer n, is there a non-reduced ring R with n non-units? For n≤100, a complete list of non-reduced decomposable rings R=∏ki=1Ri (up to cardinalities of constituent local rings Ri's) with n non-units is given. We also show that for which n, (1≤n≤7500), |Center(Γ(R))| attains the bounds in the inequality 1≤|Center(Γ(R))|≤n and for which n, (2≤n≤100), |Center(Γ(R))|
attains the value between the bounds

In this paper we will study the tight closure of a graded ideal relative to a graded Module.

Let R be a hyperring (in the sense of [8]) andM be a hypermodule on
R. In this paper we will introduce and study a class of subhypermodules
of M. We will study on intersection of this kind of subhypermodules a
give some suitable results about them. We will proceed to give some in-
teresting results about the complements, direct sums and independency
of this kind of subhypermodules

be a 3-prime near-ring with the center the present paper it is shown that a 3-prime near-ring
N is a commutative ring if and only if it admits a left multiplier F satisfying any oZ(N) and n≥1 be a fixed positive integer. Inne of the following
properties: (i)Fn([x,y])∈Z(N), (ii)Fn(x∘y)∈Z(N) (iii)Fn([x,y])±(x∘y)∈Z(N) and (iv)Fn([x,y])±x∘y∈Z(N), for all x,y∈N