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Genus of total graphs from rings: A survey

AKCE International Journal of Graphs and Combinatorics, 2018
Let R be a commutative ring. The total graph T Γ ( R ) of R is the undirected graph with vertex set R and two distinct vertices x and y are adjacent if x + y is a zero divisor in R . In this paper, we present a survey of results on the genus of T Γ ( R )
T. Tamizh Chelvam, T. Asir
doaj

Localization and Flatness in Quantale Theory

Mathematics
The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales.
George Georgescu
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Canonical bases for subalgebras of factor algebras [PDF]

Computer Science Journal of Moldova, 1999
We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Grobner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain ...
P. Nordbeck
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Reducibility of the determinant possessing variables as elements, if considered as a polynomial on a commutative ring [PDF]

, 1952
Jan Mařík
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Holographic Einstein rings of non-commutative black holes

European Physical Journal C: Particles and Fields
With the help of AdS/CFT correspondence, we derive the desired response function of QFT on the boundary of the non-commutative black hole. Using the virtual optical system with a convex lens, we obtain the Einstein rings of the black hole from the ...
Xin-Yun Hu, Xiao-Xiong Zeng, Li-Fang Li, Peng Xu +3 more
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Commutative rings over which every module has a maximal submodule [PDF]

, 1967
Ross M. Hamsher
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Commutativity theorems for nonassociative rings with a finite division ring homomorphic image [PDF]