In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms.

Usually I've seen the definition as ${M\otimes}-$ reflecting isomorphisms and preserving indecomposability. For example in On Corner type Endo-Wild algebras, Simson gives this definition and cites Drozd for it.

Thus my question: Are these two definitions equivalent? And if not, for which families of algebras are they known to be equivalent?

Specifically I'm interested in which groups are of wild representation type, but the bimodules constructed in Representation type of finite groups does not appear to preserve indecomposability.

Drozd, J.A. (1980). Tame and wild matrix problems. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg.

Simson, D., On Corner type Endo-Wild algebras, Journal of Pure and Applied Algebra, Volume 202, Issues 1–3, 2005, Pages 118-132, ISSN 0022-4049.

Bondarenko, V.M., Drozd, Y.A. Representation type of finite groups. J Math Sci 20, 2515–2528 (1982).

In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms.

Usually I've seen the definition as ${M\otimes}-$ reflecting isomorphisms and preserving indecomposability. For example in On Corner type Endo-Wild algebras, Simson gives this definition and cites Drozd for it.

Thus my question: Are these two definitions equivalent? And if not, for which families of algebras are they known to be equivalent?

Specifically I'm interested in which groups are of wild representation type, but the bimodules constructed in Representation type of finite groups does not appear to preserve indecomposability.

Drozd, J.A. (1980). Tame and wild matrix problems. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg.

Simson, D., On Corner type Endo-Wild algebras, Journal of Pure and Applied Algebra, Volume 202, Issues 1–3, 2005, Pages 118-132, ISSN 0022-4049.

Bondarenko, V.M., Drozd, Y.A. Representation type of finite groups. J Math Sci 20, 2515–2528 (1982).

In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms.

Usually I've seen the definition as ${M\otimes}-$ reflecting isomorphisms and indecomposability. For example in On Corner type Endo-Wild algebras, Simson gives this definition and cites Drozd for it.

Thus my question: Are these two definitions equivalent? And if not, for which families of algebras are they known to be equivalent?

Specifically I'm interested in which groups are of wild representation type, but the bimodules constructed in Representation type of finite groups does not appear to preserve indecomposability.

Drozd, J.A. (1980). Tame and wild matrix problems. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg.

Simson, D., On Corner type Endo-Wild algebras, Journal of Pure and Applied Algebra, Volume 202, Issues 1–3, 2005, Pages 118-132, ISSN 0022-4049.

Bondarenko, V.M., Drozd, Y.A. Representation type of finite groups. J Math Sci 20, 2515–2528 (1982).

In Tame and wild matrix problems, Drozd defines an algebra $A$ to be wild if there is an $A-k\langle x,y \rangle$-bimodule $M$, such that ${M \otimes}-$ reflects isomorphisms.

Usually I've seen the definition as ${M\otimes}-$ reflecting isomorphisms and preserving indecomposability. For example in On Corner type Endo-Wild algebras, Simson gives this definition and cites Drozd for it.

Thus my question: Are these two definitions equivalent? And if not, for which families of algebras are they known to be equivalent?

Specifically I'm interested in which groups are of wild representation type, but the bimodules constructed in Representation type of finite groups does not appear to preserve indecomposability.

Drozd, J.A. (1980). Tame and wild matrix problems. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg.

Simson, D., On Corner type Endo-Wild algebras, Journal of Pure and Applied Algebra, Volume 202, Issues 1–3, 2005, Pages 118-132, ISSN 0022-4049.

Bondarenko, V.M., Drozd, Y.A. Representation type of finite groups. J Math Sci 20, 2515–2528 (1982).