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Tag: Algebra and Number Theory

  • Complete evolution algebras are classified for two conjectures

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    What the study found The study gives positive answers to two conjectures by Camacho, Khudoyberdiyev, and Omirov about the classification of complete evolution algebras. It also reports new results on subalgebras and idempotents of evolution algebras, and it proposes a conjecture that may characterise solvable evolution algebras. Why the authors say this matters The authors…

  • Reformulation of q-middle convolution adds composition additivity

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    What the study found The authors reformulated q-convolution and q-middle convolution, which are operations used in the study of q-difference equations. They also introduced q-analogues of addition linked to gauge transformation, and found that the reformulation gives additivity for the composition of two q-middle convolutions. Why the authors say this matters The study suggests that…

  • Parameterized noetherian rings exist for each cardinal case

    Parameterized noetherian rings exist for each cardinal case

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    What the study found The study shows that for every singular cardinal, there is a valuation domain that is strictly (<α)-noetherian. For every regular cardinal, it shows a valuation domain that is strictly (<α⁺)-noetherian. Why the authors say this matters The authors say this gives a positive answer to a problem posed by Mazari–Armida under…

  • Unit-zero divisor graph built from commutative rings

    Unit-zero divisor graph built from commutative rings

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    What the study found The paper introduces the unit-zero divisor graph of a commutative ring with identity, defined using both addition and multiplication. The authors say this graph reflects two ring operations at once and examine several of its basic graph properties. Why the authors say this matters The study suggests that this graph construction…

  • Conditional bounds for Dirichlet L-function arguments and low-lying zeros

    Conditional bounds for Dirichlet L-function arguments and low-lying zeros

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    What the study found Under the generalized Riemann hypothesis, the study gives conditional bounds on the mean and mean square of the argument of Dirichlet L-functions for large prime modulus. It also reports applications to low-lying zeros and a new lower bound on the proportion of Dirichlet L-functions with zeros close to the central point.…