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Places and valuations in noncommutative ring theory /
Published 1981Subjects: “…Noncommutative rings…”
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No-go theorems for functorial localic spectra of noncommutative rings
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No−go theorems for functorial localic spectra of noncommutative rings
Published 2011Journal article -
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Some interactions between Hopf Galois extensions and noncommutative rings
Published 2022-08-01Subjects: Get full text
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Extension of Almost Primary Ideals to Noncommutative Rings and the Generalization of Nilary Ideals
Published 2023-04-01Subjects: Get full text
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On a question of herstein concerning commutators in division rings /
Published 1995Subjects: “…Noncommutative rings…”
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Relative invariants of rings : the noncommutative theory /
Published 1984Subjects: “…Noncommutative rings…”
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Reflectors and localization : application to sheaf theory /
Published 1979Subjects: “…Noncommutative rings…”
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Lightweight noncommutative key exchange protocol for IoT environments
Published 2022-09-01Subjects: Get full text
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Jacobson’s conjecture and skew PBW extensions
Published 2014-12-01Subjects: “…Noncommutative rings…”
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A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type
Published 2020-06-01“…Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry.…”
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Determinants as Combinatorial Summation Formulas over an Algebra with a Unique $n$-ary Operation
Published 2018-12-01“…In 1979-1980, the author has found the first polynomial identity for permanents over a commutative ring, and, in 2013, the polynomial identity of a new type for determinants over a noncommutative ring with associative powers. In this paper we give a general definition for determinant (the $e$-determinant) over an algebra with a unique $n$-ary $f$-operation. …”
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Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four
Published 2023-11-01“…We study the structure of self-orthogonal and self-dual codes over two non-unital rings of order four, namely, the commutative ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>=</mo><mfenced separators="" open="⟨" close="⟩"><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mspace width="0.166667em"></mspace><mo>|</mo><mspace width="0.166667em"></mspace><mn>2</mn><mi>a</mi><mo>=</mo><mn>2</mn><mi>b</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace></mrow><msup><mi>a</mi><mn>2</mn></msup><mo>=</mo><mi>b</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="italic">ab</mi><mo>=</mo><mn>0</mn></mfenced></mrow></semantics></math></inline-formula> and the noncommutative ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>=</mo><mfenced separators="" open="⟨" close="⟩"><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mspace width="0.166667em"></mspace><mo>|</mo><mspace width="0.166667em"></mspace><mn>2</mn><mi>a</mi><mo>=</mo><mn>2</mn><mi>b</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace></mrow><msup><mi>a</mi><mn>2</mn></msup><mo>=</mo><mi>a</mi><mo>,</mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mi>b</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="italic">ab</mi><mo>=</mo><mi>a</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi mathvariant="italic">ba</mi><mo>=</mo><mi>b</mi></mfenced><mo>.…”
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