The binary products of algebras with genetic realization

Dali Zangurashvili

doi:10.1515/gmj-2025-2079

Article Publicly Available

The binary products of algebras with genetic realization

This erratum corrects the original online version which can be found here: https://doi.org/10.1515/gmj-2024-2060

Dali Zangurashvili

Published/Copyright: October 28, 2025

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From the journal Georgian Mathematical Journal

Abstract

We replace the assumption in Proposition 2.4 of our article by a milder condition.

Keywords: Algebra with genetic realization; natural basis; baric algebra; Cartesian product of algebras

MSC 2020: 17D92; 18A30

We replace the assumption of Proposition 2.4 of our article [1] by a milder condition so that the proposition reads as follows:

Proposition 2.4.

Let K be either the field of real numbers or an algebraically closed field of the characteristic 0. Let A and B be baric algebras over K, and let e 1 , e 2 , … , e n and f 1 , f 2 , … , f m be seminatural bases of A and B, respectively. Then the following bases of A × B are seminatural:

( e 1 , 0 ) , ( e 2 , 0 ) , … , ( e n , 0 ) , ( a , f 1 ) , ( a , f 2 ) , … , ( a , f m )

with

a = 1 n ⁢ ∑ i = 1 n e i

and

( e 1 , b ) , ( e 2 , b ) , … , ( e n , b ) , ( 0 , f 1 ) , ( 0 , f 2 ) , … , ( 0 , f m )

with

b = 1 m ⁢ ∑ j = 1 m f j .

References

[1] D. Zangurashvili, The binary products of algebras with genetic realization, Georgian Math. J. 32 (2025), no. 3, 529–533. 10.1515/gmj-2024-2060Search in Google Scholar

Received: 2025-10-03

Accepted: 2025-10-03

Published Online: 2025-10-28

https://doi.org/10.1515/gmj-2025-2079

Keywords for this article

Algebra with genetic realization; natural basis; baric algebra; Cartesian product of algebras