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Пусть T(x,y) — тензорная алгебра (некоммутативные многочлены от двух переменных) над каким-нибудь коммутативным кольцом. Вот оказывается алгебра T(x,y)/(2x=0, 3y=0) порождается одним элементом (задача: каким?)
(а если ввести мультиградуировку, скажем deg(x):=(1,0), deg(y):=(0,1), и требовать чтобы образующие и соотношения были мультиоднородными, то одним элементом её не породить. Это потому что Z/2⊕Z/3 = Z/6)
(ну и, конечно, алгебра T(x,y)/(2x=0, 2y=0) тоже одним элементом не порождается)
Пусть T(x,y) — тензорная алгебра (некоммутативные многочлены от двух переменных) над каким-нибудь коммутативным кольцом. Вот оказывается алгебра T(x,y)/(2x=0, 3y=0) порождается одним элементом (задача: каким?)
(а если ввести мультиградуировку, скажем deg(x):=(1,0), deg(y):=(0,1), и требовать чтобы образующие и соотношения были мультиоднородными, то одним элементом её не породить. Это потому что Z/2⊕Z/3 = Z/6)
(ну и, конечно, алгебра T(x,y)/(2x=0, 2y=0) тоже одним элементом не порождается)
BY сладко стянул
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"For Telegram, accountability has always been a problem, which is why it was so popular even before the full-scale war with far-right extremists and terrorists from all over the world," she told AFP from her safe house outside the Ukrainian capital. Channels are not fully encrypted, end-to-end. All communications on a Telegram channel can be seen by anyone on the channel and are also visible to Telegram. Telegram may be asked by a government to hand over the communications from a channel. Telegram has a history of standing up to Russian government requests for data, but how comfortable you are relying on that history to predict future behavior is up to you. Because Telegram has this data, it may also be stolen by hackers or leaked by an internal employee. For Oleksandra Tsekhanovska, head of the Hybrid Warfare Analytical Group at the Kyiv-based Ukraine Crisis Media Center, the effects are both near- and far-reaching. Telegram does offer end-to-end encrypted communications through Secret Chats, but this is not the default setting. Standard conversations use the MTProto method, enabling server-client encryption but with them stored on the server for ease-of-access. This makes using Telegram across multiple devices simple, but also means that the regular Telegram chats you’re having with folks are not as secure as you may believe. Telegram has become more interventionist over time, and has steadily increased its efforts to shut down these accounts. But this has also meant that the company has also engaged with lawmakers more generally, although it maintains that it doesn’t do so willingly. For instance, in September 2021, Telegram reportedly blocked a chat bot in support of (Putin critic) Alexei Navalny during Russia’s most recent parliamentary elections. Pavel Durov was quoted at the time saying that the company was obliged to follow a “legitimate” law of the land. He added that as Apple and Google both follow the law, to violate it would give both platforms a reason to boot the messenger from its stores.
from es
