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The Quadratic Tree of a Two-Dimensional Regular Local Ring
In this survey article, we discuss recent work describing the integrally closed rings between a two-dimensional regular local ring D and its quotient...
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On the structure of semigroups whose regular elements are completely regular
We study the structure of strongly 2-chained semigroups, which can be defined alternatively as semigroups whose regular elements are completely...
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Jordan Regular Units in Rings and Group Rings
The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma, and Yadav in Comm. Algebra , 40 , No. 4, 1304–1315...
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On Total and Regular Graphs of a Polynomial
A regular graph of the ring of n × n matrices over a field is a graph whose vertices are nonsingular matrices. Two different matrices are adjacent if...
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Equivariant Grothendieck ring of a complete symmetric variety of minimal rank
We describe the G -equivariant Grothendieck ring of a regular compactification X of an adjoint symmetric space G / H of minimal rank. This extends the...
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Generalized Inverses and Units in a Unitary Ring
Let R be a unitary ring and a , b ∈ R with ab = 0. We find the 2/3 property of Drazin invertibility: if any two of a , b and a + b are Drazin invertible,...
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AN ADDITIVE BASIS FOR THE COHOMOLOGY RINGS OF REGULAR NILPOTENT HESSENBERG VARIETIES
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all...
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Von Neumann Regular Hyperrings and Applications to Real Reduced Multirings
A multiring is a ring-like structure where the sum is multivalued and a hyperring is a multiring with a strong distributive property. With every...
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Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot action of...
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LHS-spectral sequences for regular extensions of categories
In (Xu, J Pure Appl Algebra 212:2555–2569, 2008), a LHS-spectral sequence for target regular extensions of small categories is constructed. We extend...
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Structure of Regular Morphisms
This chapter is probably the most technical of all chapters of the book. The main aim of Chap. 5 is to...
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Hyper-regular graphs and high dimensional expanders
Let G = ( V, E ) be a finite graph. For d 0 > 0 we say that G is d 0 -regular, if every v ∈ V has degree d 0 . We say that G is ( d 0 , d 1 )-regular, for 0 < d 1 ...
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Self-Orthogonal Codes from Deza Graphs, Normally Regular Digraphs and Deza Digraphs
In this paper, we give constructions of self-orthogonal codes from orbit matrices of Deza graphs, normally regular digraphs and Deza digraphs in...
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Commutative Ring Extensions Defined by Perfect-Like Conditions
In 2005, Enochs, Jenda, and López-Romos extended the notion of perfect rings to n -perfect rings such that a ring is n -perfect if every flat module...
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Distance-regular Cayley graphs over dicyclic groups
The characterization of distance-regular Cayley graphs originates from the problem of identifying strongly regular Cayley graphs, or equivalently,...
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Excellent Rings and Regular Morphisms
Chapter 3 , together with Chap. 5 , is one of the most consistent...