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Near-ring congruences on seminearrings
While establishing the bijection between near-ring congruences and various types of ideals of seminearrings, different kinds of restrictions were...
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The Bloch–Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms
There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q -brackets are quasimodular...
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On when the union of two algebraic sets is algebraic
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize...
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Modules
This expository chapter covers the part of near-ring theory which offers near-ring analogues of the Jacobson-Wedderburn-Artin results from ring...
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Stability and instability of lattices in semisimple groups
Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect...
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Product Theory on Finite Elementary Abelian Groups
This chapter applies the constructions of the previous chapter to finite elementary abelian p-groups, presenting a matrix representation in which...
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Siegel Modular Forms of Degree Two and Three and Invariant Theory
This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cléry and Carel...
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Abstract Algebra and Number Theory
The word algebra takes on a very different meaning from how it is used in school. Algebra means much more than the rules of shuffling around symbols...
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Basic Theory of the Lucas Sequences
This chapter discusses the fundamental properties of Lucas sequences. Those who have worked with, or who have had an interest in, Lucas sequences...
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Cyclotomic Number Theory: Roots and Reciprocity
One of the biggest remaining generalizations in moving from the Gaussian integers to arbitrary quadratic fields is the series of results that...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Near-Rings on Groups with Low Order
This chapter considers which groups with order less than 32 may host unital near-rings.
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Problems and related results in algebraic vision and multiview geometry
This article is a survey of results in algebraic vision and multiview geometry. The starting point is the study of projective algebraic varieties...
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Commutative Monoids, Noncommutative Rings and Modules
These are the notes of a non-standard course of Algebra. It deals with elementary theory of commutative monoids and non-commutative rings. Most of...
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On the Origins, Nature, and Impact of Bourgain’s Discretized Sum-Product Theorem
We discuss the origins, nature, and development of the discretized sum-product theorem, a result which Jean Bourgain viewed as one of his most...
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A Survey of the Additive Dilogarithm
Borel’s construction of the regulator gives an injective map from the algebraic K–groups of a number field to its Deligne–Beilinson cohomology...